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<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
==Important Note(!)==<br />
An important note when using PIE is to understand how to strategically overcount and undercount, in the end making sure every element is counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem solving.<br />
<br />
== Application ==<br />
Here we will illustrate how PIE is applied with various numbers of sets.<br />
<br />
=== Two Set Example ===<br />
Assume we are given the sizes of two sets, <math>|A_1|</math> and <math>|A_2|</math>, and the size of their intersection, <math>|A_1\cap A_2|</math>. We wish to find the size of their union, <math>|A_1\cup A_2|</math>.<br />
<br />
To find the union, we can add <math>|A_1|</math> and <math>|A_2|</math>. In doing so, we know we have counted everything in <math>|A_1\cup A_2|</math> at least once. However, some things were counted twice. The elements that were counted twice are precisely those in <math> {}A_1\cap A_2 </math>. Thus, we have that:<br />
<br />
<center><math> |A_1 \cup A_2| = |A_1| + |A_2| - |A_1\cap A_2|</math>.</center><br />
<br />
=== Three Set Examples ===<br />
Assume we are given the sizes of three sets, <math>|A_1|, |A_2|,{}</math> and <math>|A_3|</math>, the size of their pairwise intersections, <math>|A_1\cap A_2|, |A_2\cap A_3|</math>, and <math>|A_3\cap A_1|</math>, and the size their overall intersection, <math>|A_1\cap A_2\cap A_3|</math>. We wish to find the size of their union, <math>|A_1\cup A_2\cup A_3|</math>.<br />
<br />
Just like in the Two Set Examples, we start with the sum of the sizes of the individual sets <math>|A_1|+|A_2|+|A_3|</math>. We have counted the elements which are in exactly one of the original three sets once, but we've obviously counted other things twice, and even other things thrice! To account for the elements that are in two of the three sets, we first subtract out <math>|A_1\cap A_2|+|A_2\cap A_3| + |A_3\cap A_1|</math>. Now we have correctly accounted for them since we counted them twice originally, and just subtracted them out once. However, the elements that are in all three sets were originally counted three times and then subtracted out three times. We have to add back in <math>|A_1\cap A_2\cap A_3|</math>. Putting this all together gives:<br />
<br />
<center><math> |A_1\cup A_2\cup A_3| = |A_1| + |A_2| + |A_3| -|A_1\cap A_2| - |A_2\cap A_3| - |A_3\cap A_1| +|A_1\cap A_2\cap A_3|</math>.</center><br />
<br />
=== Four Set Example ===<br />
==== Problem ====<br />
<br />
Six people of different heights are getting in line to buy donuts. Compute the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of height, from front to back. (2015 ARML I10)<br />
<br />
==== Solution ====<br />
<br />
Let <math>A</math> be the event that the first, second, and third people are in ordered height, <math>B</math> be the event that the second, third, and fourth people are in ordered height, <math>C</math> be the event that the third, fourth, and fifth people are in ordered height, and <math>D</math> be the event that the fourth, fifth and sixth people are in ordered height. By a combination of complementary counting and PIE, we have that our answer will be <math>720-|A|-|B|-|C|-|D|+|A\cap B|+|A\cap C|+|A\cap D|+|B\cap C|+|B\cap D|+|C\cap D|-|A\cap B\cap C|-|A\cap B\cap D|-|A\cap C\cap D|-|B\cap C\cap D|+|A\cap B\cap C\cap D|</math>. Now for the daunting task of evaluating all of this.<br />
<br />
For <math>|A|</math>, we just choose <math>3</math> people and there is only one way to put them in order, then <math>3!</math> ways to order the other three guys for <math>3!\binom{6}{3}=120</math>. Same goes for <math>|B|</math>, <math>|C|</math>, and <math>|D|</math>.<br />
<br />
Now, for <math>|A\cap B|</math>, that's just putting four guys in order. By the same logic as above, this is <math>2!\binom{6}{4}=30</math>. Again, <math>|A\cap C|</math> would be putting five guys in order, so <math>1!\binom{6}{5}=6</math>. <math>|A\cap D|</math> is just choosing <math>3</math> guys out of <math>6</math>, then <math>3</math> guys out of <math>3</math> for <math>\binom{6}{3}=20</math>. Now, <math>|B\cap C|</math> is just the same as <math>|A\cap B|</math>, so <math>30</math>, <math>|B\cap D|</math> is <math>|A\cap C|</math> so <math>6</math>, and <math>|C\cap D|</math> is <math>|A\cap B|</math> so <math>30</math>.<br />
<br />
Moving on to the next set: <math>|A\cap B\cap C|</math> is the same as <math>|A\cap C|</math> which is <math>6</math>, <math>|A\cap B\cap D|</math> is ordering everybody so <math>1</math>, <math>|A\cap C\cap D|</math> is again ordering everybody which is <math>1</math>, and <math>|B\cap C\cap D|</math> is the same as <math>|A\cap B\cap C|</math> so <math>6</math>.<br />
<br />
Finally, <math>|A\cap B\cap C\cap D|</math> is ordering everybody so <math>1</math>.<br />
<br />
Now, lets substitute everything back in. We get a massive expression of <math>720-120-120-120-120+30+6+20+30+6+30-6-1-1-6+1=\boxed{349}</math>.<br />
<br />
=== Five Set Example ===<br />
==== Problem ====<br />
<br />
There are five courses at my school. Students take the classes as follows:<br />
243 take algebra.<br />
323 take language arts.<br />
143 take social studies.<br />
241 take biology.<br />
300 take history.<br />
213 take algebra and language arts.<br />
264 take algebra and social studies.<br />
144 take algebra and biology.<br />
121 take algebra and history.<br />
111 take language arts and social studies.<br />
90 take language arts and biology.<br />
80 take language arts and history.<br />
60 take social studies and biology.<br />
70 take social studies and history.<br />
60 take biology and history.<br />
50 take algebra, language arts, and social studies.<br />
50 take algebra, language arts, and biology.<br />
50 take algebra, language arts, and history.<br />
50 take algebra, social studies, and biology.<br />
50 take algebra, social studies, and history.<br />
50 take algebra, biology, and history.<br />
50 take language arts, social studies, and biology.<br />
50 take language arts, social studies, and history.<br />
50 take language arts, biology, and history.<br />
50 take social studies, biology, and history.<br />
20 take algebra, language arts, social studies, and biology.<br />
15 take algebra, language arts, social studies, and history.<br />
15 take algebra, language arts, biology, and history.<br />
10 take algebra, social studies, biology, and history.<br />
10 take language arts, social studies, biology, and history.<br />
5 take all five.<br />
None take none. <br />
<br />
How many people are in my school?<br />
<br />
==== Solution ====<br />
Let A be the subset of students who take Algebra, L-languages, S-Social Studies, B-biology, H-history, M-the set of all students. We have:<br />
<br />
<math>|M|=|A|+|L|+|S|+|B|+|H|-|A\cap L|-|A\cap S|-|A\cap B|-|A\cap H|-|L\cap S|-|L\cap B|</math><br />
<br />
<math>-|L\cap H|-|S\cap B|-|S\cap H|-|B\cap H|+|A\cap L\cap S|+|A\cap L\cap B|+|A\cap L\cap H|+|A\cap S\cap B|+|A\cap S\cap H|</math><br />
<br />
<math>+|A\cap B\cap H|+|L\cap S\cap H|+|L\cap S \cap B|+|S\cap B\cap H|+|L \cap B\cap H|-|A\cap L\cap S\cap B|-|A\cap L\cap S\cap H|</math><br />
<br />
<math>-|A\cap L\cap B\cap H|-|A\cap S\cap B\cap H|-|L\cap S\cap B\cap H|+|A\cap L\cap S\cap B\cap H|</math><br />
<br />
<math>=243+323+143+241+300-213-264-144-121-111-90-80-60-70-60</math><br />
<br />
<math>+50+50+50+50+50+50+50+50+50+50-20-15-15-10-10+5=472</math><br />
<br />
Thus, there are <math> \boxed{472} </math> people in my school.<br />
<br />
== Statement ==<br />
If <math>(A_i)_{1\leq i\leq n}</math> are finite sets, then:<br />
<center><math> \left|\bigcup_{i=1}^n A_i\right|=\sum_{i=1}^n\left|A_i\right|<br />
-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|-\cdots\ +(-1)^{n-1} \left|A_1\cap\cdots\cap A_n\right|{}</math>.</center><br />
<br />
== Proof ==<br />
We prove that each element is counted once.<br />
<br />
Say that some element <math>X</math> is in <math>k</math> sets. Without loss of generality, these sets are <math>A_1,A_2,\dots,A_k.</math><br />
<br />
We proceed by induction. This is obvious for <math>k=1.</math><br />
<br />
If this is true for <math>k,</math> we prove this is true for <math>k+1.</math> For every set of sets not containing <math>A_{k+1}</math> with size <math>i,</math> there is a set of sets containing <math>A_{k+1}</math> with size <math>i+1.</math> In PIE, the sum of how many times these sets are counted is <math>0.</math> There is also one additional set of sets <math>\{A_{k+1}\},</math> so <math>X</math> is counted exactly once.<br />
<br />
== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\ge \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|</math>,<br />
<br />
and so on.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=135905Principle of Inclusion-Exclusion2020-10-27T00:46:05Z<p>Vsar0406: Undo revision 135751 by Mathpro12345 (talk)</p>
<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
== Application ==<br />
Here we will illustrate how PIE is applied with various numbers of sets.<br />
<br />
=== Two Set Example ===<br />
Assume we are given the sizes of two sets, <math>|A_1|</math> and <math>|A_2|</math>, and the size of their intersection, <math>|A_1\cap A_2|</math>. We wish to find the size of their union, <math>|A_1\cup A_2|</math>.<br />
<br />
To find the union, we can add <math>|A_1|</math> and <math>|A_2|</math>. In doing so, we know we have counted everything in <math>|A_1\cup A_2|</math> at least once. However, some things were counted twice. The elements that were counted twice are precisely those in <math> {}A_1\cap A_2 </math>. Thus, we have that:<br />
<br />
<center><math> |A_1 \cup A_2| = |A_1| + |A_2| - |A_1\cap A_2|</math>.</center><br />
<br />
=== Three Set Examples ===<br />
Assume we are given the sizes of three sets, <math>|A_1|, |A_2|,{}</math> and <math>|A_3|</math>, the size of their pairwise intersections, <math>|A_1\cap A_2|, |A_2\cap A_3|</math>, and <math>|A_3\cap A_1|</math>, and the size their overall intersection, <math>|A_1\cap A_2\cap A_3|</math>. We wish to find the size of their union, <math>|A_1\cup A_2\cup A_3|</math>.<br />
<br />
Just like in the Two Set Examples, we start with the sum of the sizes of the individual sets <math>|A_1|+|A_2|+|A_3|</math>. We have counted the elements which are in exactly one of the original three sets once, but we've obviously counted other things twice, and even other things thrice! To account for the elements that are in two of the three sets, we first subtract out <math>|A_1\cap A_2|+|A_2\cap A_3| + |A_3\cap A_1|</math>. Now we have correctly accounted for them since we counted them twice originally, and just subtracted them out once. However, the elements that are in all three sets were originally counted three times and then subtracted out three times. We have to add back in <math>|A_1\cap A_2\cap A_3|</math>. Putting this all together gives:<br />
<br />
<center><math> |A_1\cup A_2\cup A_3| = |A_1| + |A_2| + |A_3| -|A_1\cap A_2| - |A_2\cap A_3| - |A_3\cap A_1| +|A_1\cap A_2\cap A_3|</math>.</center><br />
<br />
=== Four Set Example ===<br />
==== Problem ====<br />
<br />
Six people of different heights are getting in line to buy donuts. Compute the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of height, from front to back. (2015 ARML I10)<br />
<br />
==== Solution ====<br />
<br />
Let <math>A</math> be the event that the first, second, and third people are in ordered height, <math>B</math> be the event that the second, third, and fourth people are in ordered height, <math>C</math> be the event that the third, fourth, and fifth people are in ordered height, and <math>D</math> be the event that the fourth, fifth and sixth people are in ordered height. By a combination of complementary counting and PIE, we have that our answer will be <math>720-|A|-|B|-|C|-|D|+|A\cap B|+|A\cap C|+|A\cap D|+|B\cap C|+|B\cap D|+|C\cap D|-|A\cap B\cap C|-|A\cap B\cap D|-|A\cap C\cap D|-|B\cap C\cap D|+|A\cap B\cap C\cap D|</math>. Now for the daunting task of evaluating all of this.<br />
<br />
For <math>|A|</math>, we just choose <math>3</math> people and there is only one way to put them in order, then <math>3!</math> ways to order the other three guys for <math>3!\binom{6}{3}=120</math>. Same goes for <math>|B|</math>, <math>|C|</math>, and <math>|D|</math>.<br />
<br />
Now, for <math>|A\cap B|</math>, that's just putting four guys in order. By the same logic as above, this is <math>2!\binom{6}{4}=30</math>. Again, <math>|A\cap C|</math> would be putting five guys in order, so <math>1!\binom{6}{5}=6</math>. <math>|A\cap D|</math> is just choosing <math>3</math> guys out of <math>6</math>, then <math>3</math> guys out of <math>3</math> for <math>\binom{6}{3}=20</math>. Now, <math>|B\cap C|</math> is just the same as <math>|A\cap B|</math>, so <math>30</math>, <math>|B\cap D|</math> is <math>|A\cap C|</math> so <math>6</math>, and <math>|C\cap D|</math> is <math>|A\cap B|</math> so <math>30</math>.<br />
<br />
Moving on to the next set: <math>|A\cap B\cap C|</math> is the same as <math>|A\cap C|</math> which is <math>6</math>, <math>|A\cap B\cap D|</math> is ordering everybody so <math>1</math>, <math>|A\cap C\cap D|</math> is again ordering everybody which is <math>1</math>, and <math>|B\cap C\cap D|</math> is the same as <math>|A\cap B\cap C|</math> so <math>6</math>.<br />
<br />
Finally, <math>|A\cap B\cap C\cap D|</math> is ordering everybody so <math>1</math>.<br />
<br />
Now, lets substitute everything back in. We get a massive expression of <math>720-120-120-120-120+30+6+20+30+6+30-6-1-1-6+1=\boxed{349}</math>.<br />
<br />
=== Five Set Example ===<br />
==== Problem ====<br />
<br />
There are five courses at my school. Students take the classes as follows:<br />
243 take algebra.<br />
323 take language arts.<br />
143 take social studies.<br />
241 take biology.<br />
300 take history.<br />
213 take algebra and language arts.<br />
264 take algebra and social studies.<br />
144 take algebra and biology.<br />
121 take algebra and history.<br />
111 take language arts and social studies.<br />
90 take language arts and biology.<br />
80 take language arts and history.<br />
60 take social studies and biology.<br />
70 take social studies and history.<br />
60 take biology and history.<br />
50 take algebra, language arts, and social studies.<br />
50 take algebra, language arts, and biology.<br />
50 take algebra, language arts, and history.<br />
50 take algebra, social studies, and biology.<br />
50 take algebra, social studies, and history.<br />
50 take algebra, biology, and history.<br />
50 take language arts, social studies, and biology.<br />
50 take language arts, social studies, and history.<br />
50 take language arts, biology, and history.<br />
50 take social studies, biology, and history.<br />
20 take algebra, language arts, social studies, and biology.<br />
15 take algebra, language arts, social studies, and history.<br />
15 take algebra, language arts, biology, and history.<br />
10 take algebra, social studies, biology, and history.<br />
10 take language arts, social studies, biology, and history.<br />
5 take all five.<br />
None take none. <br />
<br />
How many people are in my school?<br />
<br />
==== Solution ====<br />
Let A be the subset of students who take Algebra, L-languages, S-Social Studies, B-biology, H-history, M-the set of all students. We have:<br />
<br />
<math>|M|=|A|+|L|+|S|+|B|+|H|-|A\cap L|-|A\cap S|-|A\cap B|-|A\cap H|-|L\cap S|-|L\cap B|</math><br />
<br />
<math>-|L\cap H|-|S\cap B|-|S\cap H|-|B\cap H|+|A\cap L\cap S|+|A\cap L\cap B|+|A\cap L\cap H|+|A\cap S\cap B|+|A\cap S\cap H|</math><br />
<br />
<math>+|A\cap B\cap H|+|L\cap S\cap H|+|L\cap S \cap B|+|S\cap B\cap H|+|L \cap B\cap H|-|A\cap L\cap S\cap B|-|A\cap L\cap S\cap H|</math><br />
<br />
<math>-|A\cap L\cap B\cap H|-|A\cap S\cap B\cap H|-|L\cap S\cap B\cap H|+|A\cap L\cap S\cap B\cap H|</math><br />
<br />
<math>=243+323+143+241+300-213-264-144-121-111-90-80-60-70-60</math><br />
<br />
<math>+50+50+50+50+50+50+50+50+50+50-20-15-15-10-10+5=472</math><br />
<br />
Thus, there are <math> \boxed{472} </math> people in my school.<br />
<br />
== Statement ==<br />
If <math>(A_i)_{1\leq i\leq n}</math> are finite sets, then:<br />
<center><math> \left|\bigcup_{i=1}^n A_i\right|=\sum_{i=1}^n\left|A_i\right|<br />
-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|-\cdots\ +(-1)^{n-1} \left|A_1\cap\cdots\cap A_n\right|{}</math>.</center><br />
<br />
== Proof ==<br />
We prove that each element is counted once.<br />
<br />
Say that some element <math>X</math> is in <math>k</math> sets. Without loss of generality, these sets are <math>A_1,A_2,\dots,A_k.</math><br />
<br />
We proceed by induction. This is obvious for <math>k=1.</math><br />
<br />
If this is true for <math>k,</math> we prove this is true for <math>k+1.</math> For every set of sets not containing <math>A_{k+1}</math> with size <math>i,</math> there is a set of sets containing <math>A_{k+1}</math> with size <math>i+1.</math> In PIE, the sum of how many times these sets are counted is <math>0.</math> There is also one additional set of sets <math>\{A_{k+1}\},</math> so <math>X</math> is counted exactly once.<br />
<br />
== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\ge \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|</math>,<br />
<br />
and so on.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=135904Principle of Inclusion-Exclusion2020-10-27T00:43:42Z<p>Vsar0406: Undo revision 135752 by Mathpro12345 (talk)</p>
<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
== Statement ==<br />
If <math>(A_i)_{1\leq i\leq n}</math> are finite sets, then:<br />
<center><math> \left|\bigcup_{i=1}^n A_i\right|=\sum_{i=1}^n\left|A_i\right|<br />
-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|-\cdots\ +(-1)^{n-1} \left|A_1\cap\cdots\cap A_n\right|{}</math>.</center><br />
<br />
== Proof ==<br />
We prove that each element is counted once.<br />
<br />
Say that some element <math>X</math> is in <math>k</math> sets. Without loss of generality, these sets are <math>A_1,A_2,\dots,A_k.</math><br />
<br />
We proceed by induction. This is obvious for <math>k=1.</math><br />
<br />
If this is true for <math>k,</math> we prove this is true for <math>k+1.</math> For every set of sets not containing <math>A_{k+1}</math> with size <math>i,</math> there is a set of sets containing <math>A_{k+1}</math> with size <math>i+1.</math> In PIE, the sum of how many times these sets are counted is <math>0.</math> There is also one additional set of sets <math>\{A_{k+1}\},</math> so <math>X</math> is counted exactly once.<br />
<br />
== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\ge \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|</math>,<br />
<br />
and so on.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=135903Principle of Inclusion-Exclusion2020-10-27T00:43:23Z<p>Vsar0406: Undo revision 135753 by Mathpro12345 (talk)</p>
<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
== Proof ==<br />
We prove that each element is counted once.<br />
<br />
Say that some element <math>X</math> is in <math>k</math> sets. Without loss of generality, these sets are <math>A_1,A_2,\dots,A_k.</math><br />
<br />
We proceed by induction. This is obvious for <math>k=1.</math><br />
<br />
If this is true for <math>k,</math> we prove this is true for <math>k+1.</math> For every set of sets not containing <math>A_{k+1}</math> with size <math>i,</math> there is a set of sets containing <math>A_{k+1}</math> with size <math>i+1.</math> In PIE, the sum of how many times these sets are counted is <math>0.</math> There is also one additional set of sets <math>\{A_{k+1}\},</math> so <math>X</math> is counted exactly once.<br />
<br />
== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\ge \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|</math>,<br />
<br />
and so on.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=135902Principle of Inclusion-Exclusion2020-10-27T00:42:54Z<p>Vsar0406: Undo revision 135754 by Mathpro12345 (talk)</p>
<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\ge \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right|</math>,<br />
<br />
<math>\left|\bigcup_{i=1}^n A_i\right|\le \sum_{i=1}^n\left|A_i\right|-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|</math>,<br />
<br />
and so on.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=135901Principle of Inclusion-Exclusion2020-10-27T00:42:22Z<p>Vsar0406: Undo revision 135755 by Mathpro12345 (talk)</p>
<hr />
<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
<br />
== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
<br />
2011 AMC 8 Problems/Problem 6<br />
https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_6<br />
<br />
2017 AMC 10B Problems/Problem 13<br />
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_13<br />
<br />
2005 AMC 12A Problems/Problem 18<br />
https://artofproblemsolving.com/wiki/index.php/2005_AMC_12A_Problems/Problem_18<br />
<br />
== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
<br />
[[Category:Combinatorics]]</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=113778AoPS Wiki:FAQ2019-12-30T21:14:59Z<p>Vsar0406: /* Can I make more than one account? */</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
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== Alcumus ==<br />
<br />
==== How is rating computed? ====<br />
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<br />
==== I am stuck on a problem, and changing the topic does not change the problem. ====<br />
:Alcumus provides review problems to make sure you still recall information learned from the past. You may not skip these problems. <br />
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== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations.<br />
<br />
====Where are all of the mock contests?====<br />
:User-generated mock contests are now in its separate subforum, [https://artofproblemsolving.com/community/c594864_aops_mock_contests AoPS Mock Contests]. Please use that forum for creating, hosting, participating in, or recruiting writers/test solvers for mock contests.<br />
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====How can I host a mock contest?====<br />
:See posts on [https://artofproblemsolving.com/community/c594864h1168324_hi__im_interested_in_writing_a_mock_contest writing a mock contest] and [https://artofproblemsolving.com/community/c594864h1349281_tips_for_organizing_a_mock_contest Tips for Organizing a Mock Contest].<br />
<br />
== LaTeX and Asymptote ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\text{\LaTeX}</math> is a typesetting markup language and document preparation system. It is widely used for typesetting expressions containing mathematical formulae. See [https://artofproblemsolving.com/wiki/index.php/LaTeX:About LaTeX:About].<br />
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==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. You can also use our [http://artofproblemsolving.com/community/c67_test_forum Test Forum].<br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPS_Wiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Click "edit" and correct the error.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk sometimes hires a small army of college students to work as interns, graders, and teaching assistants. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==AoPS Acronyms==<br />
*'''AFK'''- Away from keyboard, inactive<br />
*'''AFAIK'''- As far as I know<br />
*'''AoPS'''- Art of Problem Solving<br />
*'''AIME'''- American Invitational Mathematics Examination<br />
*'''admin(s)'''- Administrator(s)<br />
*'''AMC'''- American Math Competitions<br />
*'''AMO'''-USA Mathematical Olympiad<br />
*'''ATM'''- At the Moment/Automated teller machine<br />
*'''brb'''- Be right back<br />
*'''BTW'''- By the way<br />
*'''CEMC''' - Centre for Mathematics and Computing<br />
*'''Combo''' - Combinatorics (Counting and Probability)<br />
*'''C&M''' - Competitions and Marathons!<br />
*'''C&P or C+P or CP''' - Counting and Probability or Contests and Programs<br />
*'''cbrt''' - Cube Root<br />
*'''DHR''' - Distinguished Honor Roll<br />
*'''EBWOP'''- Editing by way of post<br />
*'''FF'''- Fun Factory/Frivolous Forum<br />
*'''FTFY''' - Fixed that for you<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''gg'''- Good Game<br />
*'''gj'''- Good Job<br />
*'''glhf'''-Good Luck Have Fun<br />
*'''gtg''' - Got to go<br />
*'''HR''' - Honor Roll<br />
*'''HSM''' - High School Math Forum<br />
*"'HQFG''' - High Quality Fun and Games<br />
*'''ID(R or E)K'''-I Don't (Really or Even) Know<br />
*'''ID(R or E)C'''-I Don't (Really or Even) Care<br />
*'''iff'''-If and only if<br />
*'''IIRC'''- If I recall correctly<br />
*'''IKR'''- I know, right?<br />
*'''IMO'''- In my opinion (or International Math Olympiad, depending on context)<br />
*'''IMHO'''- In my humble/honest opinion <br />
*'''JK'''- Just kidding<br />
*'''JMO'''- United States of America Junior Mathematical Olympiad<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''NFL'''- Not for long/No friends left/National Football League<br />
*'''NHL'''-National Hockey League<br />
*'''mod(s)'''- Moderator(s)<br />
*'''MOEMS'''- Math Olympiads for Elementary and Middle Schools<br />
*'''MO(S)P'''- Mathematical Olympiad (Summer) Program<br />
*'''MSM'''- Middle School Math Forum<br />
*'''NIMO'''-National Internet Math Olympiad<br />
*'''NT'''- Number Theory<br />
*'''OBC'''- Online by computer<br />
*'''OMG'''- Oh My Gosh<br />
*'''OMO'''-Online Math Open<br />
*'''OP'''- Original Poster/Original Post/Original Problem, or Overpowered/Overpowering<br />
*'''QED'''- Quod erat demonstrandum, Latin for "Which was to be proven"; some English mathematicians use it as an acronym for Quite Elegantly Done<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''ro(t)fl''' - Rolling on the floor laughing<br />
*'''smh''' - Shaking my head/somehow<br />
*'''sqrt''' - Square root<br />
*'''Sticky'''- A post pinned to the top of a forum - a thing you really should read<br />
*'''ToS'''- Terms of Service - a thing you really should read<br />
*'''USA(J)MO'''- USA (Junior) Mathematical Olympiad<br />
*'''V/LA'''- Vacation or long absence/limited access<br />
*'''WDYM'''- What do you mean?<br />
*'''WIP'''- Work in progress<br />
*'''WLOG'''- Without loss of generality<br />
*'''WOOT''' - Worldwide Online Olympiad Training<br />
*'''wrt'''- With respect to<br />
*'''wtg''' - Way to go<br />
*'''tytia'''- Thank you, that is all<br />
*'''ty'''- Thank you<br />
*'''ttyl'''- Talk to you later<br />
*'''xD'''- Bursting laugh<br />
*'''TL;DR'''- Too long; don't read (a summary of the associated text)<br />
*'''yw'''- You're welcome<br />
<br />
== FTW! ==<br />
<br />
Please see the [//artofproblemsolving.com/ftw/faq For the Win! FAQ] for many common questions.<br />
<br />
== School ==<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board. Don't worry, though, classroom participation usually isn't weighted heavily.<br />
<br />
==== Is there audio or video in class? ====<br />
:There is generally no audio or video in the class. The classes are generally text and image based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity and being less pedagogically effective, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== For my homework, there is supposed to be a green bar but it's orange, why? ====<br />
<br />
:The bar turns green if and only if writing problem is attempted.<br />
<br />
==== I need more time for my homework, what should I do? ====<br />
<br />
:There is a "Request Extension" button in the homework tab of your class. This will automatically extend the due date to 2 days after the normal deadline. If you want more time you need to ask for it in the little comment box, stating the reason why you want the extension, and how much time you want. This request will be looked at by the teachers and they will decide if you get the extension or not. Note that you can only use this button 3 times. After, you will need administrator approval.<br />
:Otherwise, you can send an email to extensions@aops.com with your username, class name and ID (the number in the class page URL after https://artofproblemsolving.com/class/) and reason for extension. Someone should get back to you within a couple days.</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=113777AoPS Wiki:FAQ2019-12-30T21:14:19Z<p>Vsar0406: </p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General==<br />
<br />
<br />
==== Can I change my username? ====<br />
<br />
: AoPS typically only changes usernames for privacy reasons (e.g., your current username reveals personal information). <br />
<br />
==== Why can't I change my avatar? ====<br />
<br />
: You must be a user for two weeks before changing your avatar. You can customize your avatar by downloading a picture and changing the dimensions via computer; however, it's really hard to get a good-looking picture under the size limit. Instead, you could visit one of the many avatar shops to get one (try searching "avatar shop" in other forums on the community page).<br />
<br />
==== Something looks weird (e.g., blurry, missing line, etc.) ====<br />
<br />
: This is likely due to your browser zoom level. Please make sure your zoom level is at 100% for correct rendering of the web page. If it is at 100% and still doesn't look right, try a refresh or hard refresh. If it still shows up, follow the instructions [https://artofproblemsolving.com/community/c10h1076079_read_me_first__how_to_write_a_bug_report here] to submit a bug report about it in Site Support.<br />
<br />
==== Can I make more than one account?==== <br />
<br />
:Short answer: absolutely not.<br />
<br />
:Long answer: multiple accounts (multis) are banned on AoPS. Having more than one account leads to issues of not remembering on what account you did what. Using multiple accounts in an attempt to "game" the system, (e.g. increase rating for posts or in online games) or otherwise violate the ToS without consequences will lead to all or some of your accounts being deactivated. If you have already made additional accounts, please choose one account and stop using the others.<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Search: Solr<br />
:* Wiki: MediaWiki<br />
:* Asymptote and <math>\text{\LaTeX}</math> are generated through their respective binary packages<br />
:* Videos: YouTube<br />
:* PyWindow: Skulpt<br />
<br />
:All other parts of the website are custom built.<br />
<br />
====Can you make an AoPS App?====<br />
<br />
:There are currently no plans to make an App as the website is just as functional as an app would be on mobile phones.<br />
<br />
== Forums ==<br />
<br />
====How do I create a forum?====<br />
<br />
:To create an AoPS forum, a user must be on the AoPS community for at least 2 weeks. To create a forum, hover over the community tab, then click "My AoPS." You should now see your avatar, and a list of your friends. Now, click on the "My Forums" tab. There, you would be able to see which forum you moderate or administrate, as well as the private forums you can access. Click on the "+" button at the top right. This should lead you to a forum creating page.<br />
<br />
====Why do some posts say they were posted in the future?====<br />
:The AoPS clock is based on the official Naval Observatory time. This is considered the most accurate time. If your computer's system clock is behind the correct time, recent posts may indicate they were posted in the future. Please correct your computer's clock or enable clock synchronization so that your clock is always correct. Mac users may wish to check [http://www.macinstruct.com/node/92 Synchronize your Mac's Clock With A Time Server]. You can also check [http://www.time.gov the US offical time.]<br />
<br />
====I've lost admin access to a forum or blog I created, how do I get it back?====<br />
:Please send an email to sheriff@aops.com. They will research your request and restore admin access to your forum if appropriate.<br />
<br />
====What should I do if I find a glitch in the community?====<br />
:First, search the Site Support forum to check if your issue has already been reported. You can search here.<br />
<br />
:If your issue isn't reported, try refreshing your browser page. Most issues go away after a refresh and there is no need to report the issue unless it continues after you refresh your browser. You can refresh on most browsers in Windows with Ctrl + R and on Mac with Cmd + R. To Hard Refresh, click Shift between Ctrl/Cmd and R.<br />
<br />
:Some commonly known glitches that should not be reported are avatars appearing twice in the topic list or private message, friends appearing more than once in the friend list, the edit icon showing next to a message when it shouldn't, and not being able to search for a forum after going back a page in the community.<br />
<br />
==== How do I format my post, e.g. bold text, add URLs, etc.? ====<br />
<br />
:AoPS is based on a markup language called BBCode. A tutorial of its functions on AoPS and how to use them can be found [[BBCode:Tutorial|here]].<br />
<br />
==== How do I hide content in the forums? ====<br />
:Wrap the content you want to hide in [hide] tags. This will make a clickable label that, once clicked, will reveal the content.<br />
[hide]Content[/hide]<br />
:If you want to customize the label, instead of saying "Click here to reveal hidden text", you can do something like:<br />
[hide=Label to display]Content[/hide]<br />
<br />
:Alternatively, wrap the content you want to hide in [tip] tags. This will make a hoverable label that, once hovered over, will reveal the content.<br />
[tip]Content[/tip]<br />
:If you want to customize the label, instead of saying "Hover for tip", you can do something like:<br />
[tip=Label to display]Content[/tip]<br />
<br />
====I got the message "Too many messages." when trying to send a private message, why?====<br />
:To prevent PM spam abuse like "hvbowibvibviorybvirusbshbiuovvisuvib", users with less than five forum posts are limited to four private messages within a forty-eight hour period.<br />
<br />
==== Posting often makes me a better user, right? ====<br />
<br />
Not necessarily. The quality of your posts matter far more than the number of posts you make. In fact, if you make too many unnecessary and spammy posts, you will be considered a worse user. Those who spam after repeated warnings will have their posting privileges revoked. <br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
:Some forums, including the Test Forum, Mafia!, Fun Factory, and most user created forums, do not count toward total posts. <br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
:If you believe a post needs moderative action, you may report it by clicking the <font face="aops">Z</font> icon on the upper-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude and unproductive.<br />
<br />
==== How do I post images? ====<br />
:While AoPS forums have the ability to attach images, we do not generally recommend doing so, as we can not guarantee the images will be available through upgrades, restorations, etc. We also have limited disk space which causes us to remove attachments from time to time. Therefore, we recommend using a third party image hosting solution. There are many options, but we recommend imgur.com.<br />
<br />
:* Go to imgur.com<br />
:* Click New Post<br />
:* Upload your image<br />
:* Right click (Ctrl+Click on Mac) on your uploaded image<br />
:* Select Copy Image Location, Copy Image Address, or similar<br />
:* Paste the copied URL in to a forum or blog post surrounded by [img] ... [/img] tags<br />
<br />
====How do I become a moderator of a forum?====<br />
:The creators of user-created forums select moderators in several different ways. Contact the creator(s) of the forum for more information.<br />
<br />
:The AoPS staff will select moderators for the major forums on an as-needed basis. If the AoPS staff determines that a forum needs additional moderators, then the staff will reach out to productive users and invite them to become moderators. These are some features that the AoPS staff may consider when selecting new moderators.<br />
<br />
:* An established history of productive posting. No unproductive, spammy, or troll posts in the past several years. (For example, a high school student might have made some poor choices while in elementary school -- but then learned from those mistakes.)<br />
:* No use of \8char or other strategies to get around rules or restrictions on the forums.<br />
:* When the user reports posts, the report is useful and helpful, and the reported post (or thread, or user) really did reflect a serious issue worthy of administrators' attention. The user filled in the "Further details" field with valuable information. The user does not report the use of phrases such as "gosh, golly gee" as profanity.<br />
:* No multis.<br />
:* No backseat moderating, no posting of "\requestlock".<br />
:* When the user revives an old thread, the new post is valuable and relevant.<br />
:* The user does not use the forums to cheat on Alcumus, homework, contests, or similar activities.<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
:One needs to have at least 5 posts in order to make a blog.<br />
<br />
==== How do I make my blog look nice? ====<br />
:Many AoPSers make their blogs look nice by applying CSS, which is a high-level stylesheet language. This can be done by typing code into the CSS box in the Blog Control Panel.<br />
<br />
== Alcumus ==<br />
<br />
==== How is rating computed? ====<br />
:The rating is more of a prediction of what percentage of problems in the topic the Alcumus engine believes you will get correct. As you get more and more correct, the rating will go up slower and slower. However, if you are predicted to get most correct, and you miss one or two problems, the rating, or prediction of percentage correct, will go down.<br />
<br />
==== I am stuck on a problem, and changing the topic does not change the problem. ====<br />
:Alcumus provides review problems to make sure you still recall information learned from the past. You may not skip these problems. <br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations.<br />
<br />
====Where are all of the mock contests?====<br />
:User-generated mock contests are now in its separate subforum, [https://artofproblemsolving.com/community/c594864_aops_mock_contests AoPS Mock Contests]. Please use that forum for creating, hosting, participating in, or recruiting writers/test solvers for mock contests.<br />
<br />
====How can I host a mock contest?====<br />
:See posts on [https://artofproblemsolving.com/community/c594864h1168324_hi__im_interested_in_writing_a_mock_contest writing a mock contest] and [https://artofproblemsolving.com/community/c594864h1349281_tips_for_organizing_a_mock_contest Tips for Organizing a Mock Contest].<br />
<br />
== LaTeX and Asymptote ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\text{\LaTeX}</math> is a typesetting markup language and document preparation system. It is widely used for typesetting expressions containing mathematical formulae. See [https://artofproblemsolving.com/wiki/index.php/LaTeX:About LaTeX:About].<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. You can also use our [http://artofproblemsolving.com/community/c67_test_forum Test Forum].<br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPS_Wiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Click "edit" and correct the error.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk sometimes hires a small army of college students to work as interns, graders, and teaching assistants. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==AoPS Acronyms==<br />
*'''AFK'''- Away from keyboard, inactive<br />
*'''AFAIK'''- As far as I know<br />
*'''AoPS'''- Art of Problem Solving<br />
*'''AIME'''- American Invitational Mathematics Examination<br />
*'''admin(s)'''- Administrator(s)<br />
*'''AMC'''- American Math Competitions<br />
*'''AMO'''-USA Mathematical Olympiad<br />
*'''ATM'''- At the Moment/Automated teller machine<br />
*'''brb'''- Be right back<br />
*'''BTW'''- By the way<br />
*'''CEMC''' - Centre for Mathematics and Computing<br />
*'''Combo''' - Combinatorics (Counting and Probability)<br />
*'''C&M''' - Competitions and Marathons!<br />
*'''C&P or C+P or CP''' - Counting and Probability or Contests and Programs<br />
*'''cbrt''' - Cube Root<br />
*'''DHR''' - Distinguished Honor Roll<br />
*'''EBWOP'''- Editing by way of post<br />
*'''FF'''- Fun Factory/Frivolous Forum<br />
*'''FTFY''' - Fixed that for you<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''gg'''- Good Game<br />
*'''gj'''- Good Job<br />
*'''glhf'''-Good Luck Have Fun<br />
*'''gtg''' - Got to go<br />
*'''HR''' - Honor Roll<br />
*'''HSM''' - High School Math Forum<br />
*"'HQFG''' - High Quality Fun and Games<br />
*'''ID(R or E)K'''-I Don't (Really or Even) Know<br />
*'''ID(R or E)C'''-I Don't (Really or Even) Care<br />
*'''iff'''-If and only if<br />
*'''IIRC'''- If I recall correctly<br />
*'''IKR'''- I know, right?<br />
*'''IMO'''- In my opinion (or International Math Olympiad, depending on context)<br />
*'''IMHO'''- In my humble/honest opinion <br />
*'''JK'''- Just kidding<br />
*'''JMO'''- United States of America Junior Mathematical Olympiad<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''NFL'''- Not for long/No friends left/National Football League<br />
*'''NHL'''-National Hockey League<br />
*'''mod(s)'''- Moderator(s)<br />
*'''MOEMS'''- Math Olympiads for Elementary and Middle Schools<br />
*'''MO(S)P'''- Mathematical Olympiad (Summer) Program<br />
*'''MSM'''- Middle School Math Forum<br />
*'''NIMO'''-National Internet Math Olympiad<br />
*'''NT'''- Number Theory<br />
*'''OBC'''- Online by computer<br />
*'''OMG'''- Oh My Gosh<br />
*'''OMO'''-Online Math Open<br />
*'''OP'''- Original Poster/Original Post/Original Problem, or Overpowered/Overpowering<br />
*'''QED'''- Quod erat demonstrandum, Latin for "Which was to be proven"; some English mathematicians use it as an acronym for Quite Elegantly Done<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''ro(t)fl''' - Rolling on the floor laughing<br />
*'''smh''' - Shaking my head/somehow<br />
*'''sqrt''' - Square root<br />
*'''Sticky'''- A post pinned to the top of a forum - a thing you really should read<br />
*'''ToS'''- Terms of Service - a thing you really should read<br />
*'''USA(J)MO'''- USA (Junior) Mathematical Olympiad<br />
*'''V/LA'''- Vacation or long absence/limited access<br />
*'''WDYM'''- What do you mean?<br />
*'''WIP'''- Work in progress<br />
*'''WLOG'''- Without loss of generality<br />
*'''WOOT''' - Worldwide Online Olympiad Training<br />
*'''wrt'''- With respect to<br />
*'''wtg''' - Way to go<br />
*'''tytia'''- Thank you, that is all<br />
*'''ty'''- Thank you<br />
*'''ttyl'''- Talk to you later<br />
*'''xD'''- Bursting laugh<br />
*'''TL;DR'''- Too long; don't read (a summary of the associated text)<br />
*'''yw'''- You're welcome<br />
<br />
== FTW! ==<br />
<br />
Please see the [//artofproblemsolving.com/ftw/faq For the Win! FAQ] for many common questions.<br />
<br />
== School ==<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board. Don't worry, though, classroom participation usually isn't weighted heavily.<br />
<br />
==== Is there audio or video in class? ====<br />
:There is generally no audio or video in the class. The classes are generally text and image based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity and being less pedagogically effective, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== For my homework, there is supposed to be a green bar but it's orange, why? ====<br />
<br />
:The bar turns green if and only if writing problem is attempted.<br />
<br />
==== I need more time for my homework, what should I do? ====<br />
<br />
:There is a "Request Extension" button in the homework tab of your class. This will automatically extend the due date to 2 days after the normal deadline. If you want more time you need to ask for it in the little comment box, stating the reason why you want the extension, and how much time you want. This request will be looked at by the teachers and they will decide if you get the extension or not. Note that you can only use this button 3 times. After, you will need administrator approval.<br />
:Otherwise, you can send an email to extensions@aops.com with your username, class name and ID (the number in the class page URL after https://artofproblemsolving.com/class/) and reason for extension. Someone should get back to you within a couple days.</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_12A_Problems/Problem_7&diff=1110372002 AMC 12A Problems/Problem 72019-11-09T23:33:14Z<p>Vsar0406: /* Solution 1 */</p>
<hr />
<div>{{duplicate|[[2002 AMC 12A Problems|2002 AMC 12A #7]] and [[2002 AMC 10A Problems|2002 AMC 10A #7]]}}<br />
<br />
<br />
==Problem==<br />
<br />
A <math>45^\circ</math> arc of circle A is equal in length to a <math>30^\circ</math> arc of circle B. What is the ratio of circle A's area and circle B's area?<br />
<br />
<math>\text{(A)}\ 4/9 \qquad \text{(B)}\ 2/3 \qquad \text{(C)}\ 5/6 \qquad \text{(D)}\ 3/2 \qquad \text{(E)}\ 9/4</math><br />
<br />
==Solutions==<br />
===Solution 1===<br />
Let <math>r_1</math> and <math>r_2</math> be the radii of circles <math>A</math> and<math> B</math>, respectively. <br />
<br />
It is well known that in a circle with radius <math> r </math>, a subtended arc opposite an angle of <math>\theta</math> degrees has length <math>\frac{\theta}{360} \cdot 2\pi r</math>. <br />
<br />
Using that here, the arc of circle A has length <math>\frac{45}{360}\cdot2\pi{r_1}=\frac{r_1\pi}{4}</math>. The arc of circle B has length <math>\frac{30}{360} \cdot 2\pi{r_2}=\frac{r_2\pi}{6}</math>. We know that they are equal, so <math>\frac{r_1\pi}{4}=\frac{r_2\pi}{6}</math>, so we multiply through and simplify to get <math>\frac{r_1}{r_2}=\frac{2}{3}</math>. As all circles are similar to one another, the ratio of the areas is just the square of the ratios of the radii, so our answer is <math>\boxed{\text{(A)}\ 4/9}</math>.<br />
<br />
===Solution 2===<br />
The arc of circle <math>A</math> is <math>\frac{45}{30}=\frac{3}{2}</math> that of circle <math>B</math>.<br />
<br />
The circumference of circle <math>A</math> is <math>\frac{2}{3}</math> that of circle <math>B</math> (<math>B</math> is the larger circle).<br />
<br />
The radius of circle <math>A</math> is <math>\frac{2}{3}</math> that of circle <math>B</math>.<br />
<br />
The area of circle <math>A</math> is <math>{\left(\frac{2}{3}\right)}^2=\boxed{\text{(A)}\ 4/9}</math> that of circle <math>B</math>.<br />
<br />
==See Also==<br />
{{AMC12 box|year=2002|ab=A|num-b=6|num-a=8}}<br />
{{AMC10 box|year=2002|ab=A|num-b=6|num-a=8}}<br />
<br />
[[Category:Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=User:Azjps/geogebra&diff=110385User:Azjps/geogebra2019-10-17T22:49:52Z<p>Vsar0406: /* Functions and Integrals */</p>
<hr />
<div>'''Gallery of examples''': The following [[Asymptote (Vector Graphics Language)|Asymptote]] codes were all generated from [[Geogebra]] files (File > Export > Graphics View as Asymptote ...). It is available in the current release of the Geogebra 4.0 Beta version. To download Geogebra 4.0, go [http://www.geogebra.org/forum/viewtopic.php?f=22&t=1387 here] and either choose the webstart (direct) version or choose one of the 3.9 version offline installers (as beta versions, there may unfixed bugs, although the versions are for the most part stable.)<br />
<br />
== Documentation ==<br />
Here is a fairly simple example that breaks down the contents of the output code, with Fill type set at "By layering".<br />
<br />
<asy><br />
/* Geogebra to Asymptote conversion, documentation at userscripts.org/scripts/show/72997 */<br />
import graph; size(14.26cm); <br />
real labelscalefactor = 0.5; /* changes label-to-point distance */<br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */<br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
<br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
Label laxis; laxis.p = fontsize(10); string xaxislabel (real x) {int n=round(x/pi); if(n==-1) return "$-\pi$"; if(n==1) return "$\pi$"; if(n==0) return "$0$"; return "$" + string(n) + "\pi$";} string yaxislabel (real x) {return "$" + string(x) + "\,\mathrm{}$";} <br />
xaxis("$x$",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */<br />
/* dots and labels */<br />
label("$f$",(-6.12,-0.12),NE * labelscalefactor); <br />
label("$a = 2$",(1.46,0.24),NE * labelscalefactor,zzttqq); <br />
dot((-3.14,0),dotstyle); <br />
label("$A$",(-3.06,0.12),NE * labelscalefactor); <br />
dot((2.2,2.04),dotstyle); <br />
dot((4.5,2.08),dotstyle); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
/* end of picture */<br />
</asy><br />
<br />
Here is the Asymptote code produced: (with some spacing added)<br />
<br />
<pre><br />
/* Geogebra to Asymptote conversion, documentation at userscripts.org/scripts/show/72997 */<br />
import graph; size(14.26cm); <br />
real labelscalefactor = 0.5; /* changes label-to-point distance */<br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */<br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
<br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
Label laxis; laxis.p = fontsize(10); <br />
string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} <br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
<br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} <br />
pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */<br />
<br />
/* dots and labels */<br />
label("<math>f</math>",(-6.12,-0.12),NE * labelscalefactor); <br />
label("<math>a = 2</math>",(1.46,0.24),NE * labelscalefactor,zzttqq); <br />
dot((-3.14,0),dotstyle); <br />
label("<math>A</math>",(-3.06,0.12),NE * labelscalefactor); <br />
dot((2.2,2.04),dotstyle); <br />
dot((4.5,2.08),dotstyle); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
/* end of picture */<br />
</pre><br />
<br />
Here is a line-by-line explanation: (<math>\texttt{/* COMMENT */}</math> are comments that are not read by the Asymptote engine.)<br />
<br />
<math>\texttt{import graph; size(14.26cm); }</math> are the opening commands: any files that need to be imported (in this case, [http://asymptote.sourceforge.net/doc/graph.html graph]), followed by the horizontal size in centimeters, as shown by the Export to Asymptote window. <br />
<br />
<math>\texttt{real labelscalefactor = 0.5; /* changes label-to-point distance */}</math> This variable scales the distance that labels are from their defined locations on the Geogebra window. This is due to an innate difference in the Asymptote and Geogebra treatment of labels: Geogebra positions labels with respect to a corner of the label, but Asymptote positions labels with respect to the center. Also, both have different default font sizes. The larger the value of <math>\texttt{labelscalefactor}</math>, the farther the Asymptote labels are dislocated from their respective points. Usually, <math>\texttt{labelscalefactor}</math> will have to be lowered to better position the labels (truer for longer labels). In concise mode, this variable is abbreviated as <math>\texttt{lsf}</math>.<br />
<br />
<pre><br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
</pre><br />
<br />
These are the definition of the default pens to use. <math>\texttt{dps}</math> stands for default pen style and produces the default pen style. <math>\texttt{dotstyle}</math> stands for the default dot style. In concise mode, the latter is abbreviated as <math>\texttt{ds}</math>, and in cse5, this option is completely replaced by the pen <math>\texttt{pointpen}</math>.<br />
<br />
<code>real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */ }</code><br />
<br />
As the comment suggests, these four variables define the boundaries of the picture (in the units of the picture). Rays and lines that go out of the picture are defined in terms of these variables, as well as the clip window. Thus, changing these variables should keep intact most of the Asymptote contents.<br />
<br />
<code><br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
</code><br />
<br />
These pens are custom defined colors, which are actually defined by hexadecimal values of the associated colors. The colors can be changed in this line (changing a specific shade to a darker shade, for example). <br />
<br />
<code><br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
</code><br />
<br />
This <math>\texttt{filldraw}</math> command draws a square in the picture. Of note is that if the axes are defined in terms of pi, then some coordinates are defined in terms of the Asymptote variable <math>\texttt{pi}</math>. The command changes to <math>\texttt{draw}</math> if the Fill type is set to "None". <br />
<br />
<pre><br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
</pre><br />
<br />
Some commands have to be defined with respect to a function. <math>\texttt{f2}</math> returns the <math>\sin(x)</math> function, and the <math>\texttt{graph}</math> command draws <math>\texttt{f2}</math> from <math>x = 0</math> to <math>x = \pi</math>.<br />
<br />
<pre><br />
Label laxis; laxis.p = fontsize(10); <br />
string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} <br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
</pre><br />
<br />
These commands draw the axes. The <math>\texttt{laxis}</math> label specifies the label styles of the axes (e.g., the field <math>\texttt{laxis.p}</math> defines the desired font pen). <br />
<br />
The next line, the <pre>string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} </pre> are functions that define the labels for both axes. These are abbreviated as <math>\texttt{xlbl, ylbl}</math> in the concise mode. The first defines axes with labels with respect to <math>\pi</math>, and it formats the labels so that the <math>0</math> label simply outputs <math>0</math> instead of <math>0\pi</math>, and <math> \pm \pi</math> instead of <math> \pm 1\pi</math>. Finally, <br />
<br />
<pre><br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
</pre><br />
<br />
are the commands that actually construct the xaxis and the yaxis. For documentation, see [http://asymptote.sourceforge.net/doc/graph.html here].<br />
<br />
The next block of code does the actual construction of the geometric figures. <pre><br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */ </pre> The first line <tt>real f1 (real x) {return sin(x);} </tt> defines the <tt>sin()</tt> function to be drawn, and the next line <tt>draw(graph(f1,-6.21,8.03)); </tt> actually draws the graph to the diagram. The <tt>graph()</tt> command comes from the Asymptote <tt>graph</tt> [http://asymptote.sourceforge.net/doc/graph.html package]. The next few lines draw several line segments. The attribute <tt>zzttqq</tt> is a pen whose color is mapped from some rgb value (with conversions <tt>... 8 = y, 9 = z, a = a, b = b, ... </tt>).<br />
<br />
== Options ==<br />
An outline of the different available options. <br />
<br />
(The first three options are related and automatically update with respect to eath other).<br />
<br />
'''X/Y Units (cm)''': Indicates how many units in the picture correspond to 1 centimeter.<br />
<br />
'''Picture width/height''': Indicates what size the Asymptote output should be, in centimeters.<br />
<br />
'''xmin/xmax/ymin/ymax''': Indicates the dimensions of the picture in the picture's coordinates. <br />
<br />
(The next options change other features).<br />
<br />
'''Font size''': Changes the default font size. The value defaults at 10pt, but I personally recommend 7pt for any file with multiple text lines, which more closely approximates the size of the font in the Geogebra window. <br />
<br />
'''Fill type''': This includes four options as to how Geogebra elements with different fill colors should be implemented:<br />
<br />
* None: No fills are drawn.<br />
* Only opaque fills. This will only cause filled objects with opaque transparencies, which are arbitrarily defined as shapes with transparency alpha values greater than 0.9 (on a 0 to 1, 1 being fully opaque, scale), to appear filled.<br />
* With opacity pen. This uses the opacity() pen to draw transparency fills. This option does not work on the AoPS forums.<br />
* By layering (my personal preference). Filled objects have "fake transparency" where filled objects are simply drawn before any other objects are drawn, and transparencies just cause a lighter shade. However, filled objects will override other filled objects, and so there is no "darker" transparencies along intersecting regions.<br />
<br />
'''Concise code''': This produces shorter Asymptote code. Some of the changes between non-concise and concise code:<br />
<br />
* In non-concise code, most new commands have their own line. In concise code, there are at most about 8 lines of code. <br />
* Abbreviations are used for certain variables (labelscalefactor to lsf, xaxislabel to xlbl, gridx to gx, and so forth). <br />
* Pen colors are produced with a single line of pen declarations. <br />
* Functions are re-used where possible.<br />
* Less spacing. <br />
<br />
The advantages of concise code:<br />
<br />
* Less code to examine.<br />
* Non-concise code will usually not render on the AoPS forums due to size limits.<br />
* Guide to customizing code should be in the following posts.<br />
<br />
The disadvantages of concise code:<br />
<br />
* More difficult to read (especially without experience with my style of coding), exacerbated by lack of spacing.<br />
* No documentation comments.<br />
* Difficult to read through from given code window, requires wrap-around to read effectively.<br />
<br />
'''Concise with cse5''': There is also a cse5 option that allows the code to be further compactified with help with the cse5 package (see the stickies in this forum). <br />
<br />
* In non-concise code, most new commands have their own line. In cse5 code, there are at most about 8 lines of code. <br />
* Abbreviations are used for certain variables (labelscalefactor to lsf, xaxislabel to xlbl, gridx to gx, and so forth). <br />
* Pairs are given names and produced in a single line; color pens are also produced in a single line.<br />
* Functions are re-used where possible.<br />
* Command shortcuts, such as MP() and D() are used extensively.<br />
* Almost no spacing. <br />
<br />
The advantages of cse5 code:<br />
<br />
* Less code to examine.<br />
* With the exception of excessively complicated diagrams, will almost always fit within AoPS size restrictions.<br />
* Guide to customizing code should be in the following posts.<br />
* Allows more customization; changing a declared point and pen will reflect changes across the code. <br />
<br />
The disadvantages of cse5 code:<br />
<br />
* Extremely difficult to read (especially without experience with my style of coding), exacerbated by lack of spacing and short commands.<br />
* No documentation comments.<br />
* Difficult to read through from given code window, requires wrap-around to read effectively.<br />
* May occasionally draw skinny points and lines, due to default pathpen and pointpen attributes. <br />
<br />
My personal recommendation is the concise code for producing quick sketches (cse5 for large quick sketches), and the non-concise code otherwise.<br />
<br />
'''Grayscale''': Uses monochromatic scale to produce all output. <br />
<br />
'''Show Axes/Grid''' (default checked): Show or hide the axes and the grid.<br />
<br />
'''Keep dot colors''': Geogebra defaults free points to a blue color and semi-fixed points to a light blue color. Without this option checked, the Asymptote code will automatically set points to the default color (black). With checked, the Asymptote code will include the point colors as shown in the Geogebra window.<br />
<br />
'''Use point names''': (to do) In the Asymptote code, store points in <math>\texttt{pair}</math> variables rather than by write out by coordinates. Done by default for concise cse5 code.<br />
<br />
== Points ==<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-5.8,xmax=5.8,ymin=-2.2,ymax=5.72; <br />
pen wwqqqq=rgb(0.4,0,0), xdxdff=rgb(0.49,0.49,1), uququq=rgb(0.25,0.25,0.25), ffqqtt=rgb(1,0,0.2);<br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis("$x$",-5.8,5.8,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); yaxis("$y$",-3.22,5.72,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); draw(shift((-4,0))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),xdxdff); draw(circle((-3,0),0.11),xdxdff); draw(shift((-2,0))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0)),xdxdff); fill(shift((-1,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),xdxdff); draw(shift((0,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),uququq); fill(shift((1,0))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((2,0))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((3,0))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((4,0))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); draw(shift((-4,1))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),blue); draw(circle((-3,1),0.11),blue); draw(shift((-2,1))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0)),blue); fill(shift((-1,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),blue); draw(shift((0,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),xdxdff); fill(shift((1,1))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((2,1))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((3,1))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((4,1))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); draw(shift((-4,2))*scale(0.18)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),ffqqtt); draw(circle((-3,2),0.18),ffqqtt); draw(shift((-2,2))*scale(0.18)*((0,1)--(0,-1)^^(1,0)--(-1,0)),ffqqtt); fill(shift((-1,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),ffqqtt); draw(shift((0,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),ffqqtt); fill(shift((1,2))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((2,2))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((3,2))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((4,2))*rotate(180)*scale(0.25)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); <br />
dot((-5,0),xdxdff); label("$A$",(-4.92,0.12),NE*lsf,xdxdff); label("$B$",(-3.92,-0.12),NE*lsf,xdxdff); label("$C$",(-2.92,0.12),NE*lsf,xdxdff); label("$D$",(-1.92,0.12),NE*lsf,xdxdff); label("$E$",(-0.92,0.12),NE*lsf,xdxdff); label("$F$",(0.08,0.12),NE*lsf,uququq); label("$G$",(1.08,0.12),NE*lsf,xdxdff); label("$H$",(2.08,0.12),NE*lsf,xdxdff); label("$I$",(3.08,0.12),NE*lsf,xdxdff); label("$J$",(4.08,0.12),NE*lsf,xdxdff); dot((5,0),linewidth(1pt)+xdxdff); label("$K$",(5.08,0.04),NE*lsf,xdxdff); dot((-5,1),blue); label("$L$",(-4.92,1.12),NE*lsf,blue); label("$M$",(-3.92,1.12),NE*lsf,blue); label("$N$",(-2.92,1.12),NE*lsf,blue); label("$O$",(-1.92,1.12),NE*lsf,blue); label("$P$",(-0.92,1.12),NE*lsf,blue); label("$Q$",(0.08,1.12),NE*lsf,xdxdff); label("$R$",(1.08,1.12),NE*lsf,blue); label("$S$",(2.08,1.12),NE*lsf,blue); label("$T$",(3.08,1.12),NE*lsf,blue); label("$U$",(4.08,1.12),NE*lsf,blue); dot((5,1),blue); label("$V$",(5.08,1.12),NE*lsf,blue); dot((-5,2),blue); dot((5,2),linewidth(5pt)+blue); label("$I_1$",(5.08,2.2),NE*lsf,blue); dot((-5,3),blue); dot((-5,4),blue); dot((-5,3.5),uququq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> <br />
Support for drawing different options of points, along with point labeling. <br />
<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-5.8,xmax=5.8,ymin=-3.22,ymax=5.72; <br />
pen wwqqqq=rgb(0.4,0,0), ffqqtt=rgb(1,0,0.2);<br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis("$x$",-5.8,5.8,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); yaxis("$y$",-3.22,5.72,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); draw(shift((-4,0))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,0),0.11)); draw(shift((-2,0))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,0))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,0))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,0))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,0))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw(shift((-4,1))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,1),0.11)); draw(shift((-2,1))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,1))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,1))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,1))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,1))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw(shift((-4,2))*scale(0.18)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,2),0.18)); draw(shift((-2,2))*scale(0.18)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,2))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,2))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,2))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,2))*rotate(180)*scale(0.25)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw((-4,3)--(-4,4),ffqqtt); <br />
dot((-5,0),ds); label("$A$",(-4.92,0.12),NE*lsf); label("$B$",(-3.92,0.12),NE*lsf); label("$C$",(-2.92,0.12),NE*lsf); label("$D$",(-1.92,0.12),NE*lsf); label("$E$",(-0.92,0.12),NE*lsf); label("$F$",(0.08,0.12),NE*lsf); label("$G$",(1.08,0.12),NE*lsf); label("$H$",(2.08,0.12),NE*lsf); label("$I$",(3.08,0.12),NE*lsf); label("$J$",(4.08,0.12),NE*lsf); dot((5,0),linewidth(1pt)+ds); label("$K$",(5.08,0.04),NE*lsf); dot((-5,1),ds); label("$L$",(-4.92,1.12),NE*lsf); label("$M$",(-3.92,1.12),NE*lsf); label("$N$",(-2.92,1.12),NE*lsf); label("$O$",(-1.92,1.12),NE*lsf); label("$P$",(-0.92,1.12),NE*lsf); label("$Q$",(0.08,1.12),NE*lsf); label("$R$",(1.08,1.12),NE*lsf); label("$S$",(2.08,1.12),NE*lsf); label("$T$",(3.08,1.12),NE*lsf); label("$U$",(4.08,1.12),NE*lsf); dot((5,1),ds); label("$V$",(5.08,1.12),NE*lsf); dot((-5,2),ds); dot((5,2),linewidth(5pt)+ds); label("$I_1$",(5.08,2.2),NE*lsf); dot((-5,3),ds); dot((-5,4),ds); dot((-5,3.5),ds); dot((-4,3),ds); dot((-4,4),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Also includes an option to remove the coloring of just points (to avoid Geogebra's default of using different colors for different classes of fixed points). <br />
<br />
<br />
<geogebra>1c89b124bb471a351bc108d34f8096d1f892e012</geogebra> (Note, the version of Geogebra here does not support different dot styles.)<br />
<br />
<br />
Also has support for different types of axes: bold, with arrows, different colors, different labelling schemes (including with <math>\pi</math> labels as in the next example). Also supports drawing of grid (with for loop constructions). There is a checkbox option to show and hide axes and grids. <br />
<br />
Known bugs:<br />
<br />
* Labels may be displaced more from points than shown in Geogebra window. This is not really a bug but a font problem, since Asymptote will write the labels in LaTeX, which has a different size from normal text. The recommended solution is to decrease the font size to fontsize(8) or fontsize(7).<br />
* Leaving <b>Keep Dot Colors()</b> unchecked will color as black any labels which are a single character long and set to the default shade of blue for new points (presumably all such labels will be dot labels, which is the desired behavior).<br />
* Some of the point styles might not be perfectly accurate when zoomed in. <br />
* In cse5 mode, certain dots will appear smaller (default pointpen nature of cse5, not fixing).<br />
<br />
=== Axes ===<br />
There is support for drawing the x and y axes of the diagram (indeed, without <b>Show Axes/Grid</b> unchecked, and assuming the axes are visible in the Geogebra window, then the axes will be drawn). However, there are several bugs:<br />
* The Asymptote code will remove the tick labels for <math>0</math>. One can undo this by removing the attribute <tt>NoZero</tt> for the <tt>xaxis(), yaxis()</tt> commands. The reason is that the zero labels are not positioned well in Asymptote (indeed, the Geogebra tick labels for <math>0</math>, or whatever the intersection point is, are shifted slightly)<br />
* The location where the label of the axes (typically "x" or "y") will by default appear in the first quadrant ("x" above the x-axis, "y" to the right of the y-axis). In Asymptote, the labels appear in the exact opposite locations ("x" below the x-axis, "y" to the left of the y-axis). Low priority bug which is unlikely to be fixed.<br />
* There is no (easy) support in Asymptote for having the x or y axes intersect at any point other than the origin. In GeoGebra, one can use the <b>Crossing at</b> textbox under Properties to change where the x-axis and y-axis intersects. <br />
* Geogebra recognizes near-multiples of <math>\pi</math> in axis tick distances; for example, if you enter an axis tick distance of <math>\pi/3 \approx 1.047\ldots</math>, Geogebra automatically renders it as <math>\pi</math> instead of <math>3.14\ldots</math>. There's no easy way to do it in Asymptote (if you do want to try and mimic the behavior, manually add a labelling function which checks to see if tick labels are sufficient close to an integer multiple of <math>\pi</math>. The code is too long to be worth included in general). Also, while <math>\pi/2</math> labels are implemented, <math>\pi/4</math> labels are soon to be introduced and have not been implemented.<br />
<br />
== Functions and Integrals ==<br />
<asy><br />
import graph; size(15.36cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-7.3,xmax=8.06,ymin=-1.44,ymax=5.2; <br />
pen ttqqzz=rgb(0.2,0,0.6), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0);<br />
real f2(real x){return 2+2*cos(2*x+pi);} filldraw(graph(f2,-6.28,-3.14)--(-3.14,0)--(-6.28,0)--cycle,fueaev,zzttqq); filldraw(box((-3.14,0),(-2.51,0)),fueaev,zzttqq); filldraw(box((-2.51,0),(-1.88,1.38)),fueaev,zzttqq); filldraw(box((-1.88,0),(-1.26,3.62)),fueaev,zzttqq); filldraw(box((-1.26,0),(-0.63,1.38)),fueaev,zzttqq); filldraw(box((-0.63,0),(0,0)),fueaev,zzttqq); filldraw(box((0,0),(0.63,1.38)),fueaev,zzttqq); filldraw(box((0.63,0),(1.26,3.62)),fueaev,zzttqq); filldraw(box((1.26,0),(1.88,4)),fueaev,zzttqq); filldraw(box((1.88,0),(2.51,3.62)),fueaev,zzttqq); filldraw(box((2.51,0),(pi,1.38)),fueaev,zzttqq); filldraw((pi,0)--(3.77,0)--(3.77,1.38)--(pi,0)--cycle,fueaev,zzttqq); filldraw((3.77,0)--(4.4,0)--(4.4,3.62)--(3.77,1.38)--cycle,fueaev,zzttqq); filldraw((4.4,0)--(5.03,0)--(5.03,3.62)--(4.4,3.62)--cycle,fueaev,zzttqq); filldraw((5.03,0)--(5.65,0)--(5.65,1.38)--(5.03,3.62)--cycle,fueaev,zzttqq); filldraw((5.65,0)--(6.28,0)--(6.28,0)--(5.65,1.38)--cycle,fueaev,zzttqq); <br />
Label laxis; laxis.p=fontsize(10); string xlbl(real x){int n=round(x/pi); if(n==-1) return "$-\pi$"; if(n==1) return "$\pi$"; if(n==0) return "$0$"; return "$"+string(round(x/pi))+"\pi$";} <br />
xaxis("$\theta$",-7.3,8.06,linewidth(1.2),Ticks(laxis,xlbl,Step=3.141592653589793,Size=2),Arrows(6),above=true); yaxis(-1.44,5.2,linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); real f1(real x){return 2+2*cos(2*x+pi);} draw(graph(f1,-7.29,8.05),linewidth(1.6)+ttqqzz); label("$2 + 2 \cos(2x + \pi)$",(-7.14,4.1),NE*lsf,ttqqzz); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Allows most functions and can draw integrals and Riemman-like sums. Above, the function is given by <math>f(x) = 2+2\cos(2x)</math>; the four shaded regions are drawn using the commands '''Integral[f,-2pi,-pi], LowerSum[f,-pi,0,5], UpperSum[f,0,pi,5],''' and '''TrapezoidalSum[f,pi,2pi,5]'''. <br />
<geogebra>6636ccd3479762307d932c319db7ec1998236a4c</geogebra> <br />
<br />
Known bugs:<br />
* May capitalize certain functions (like trigonometric functions). Please let me know if this happens.<br />
* Certain functions recognized by Geogebra might not be recognized by Asymptote.<br />
* Integrals/Sums drawn over functions that reach undefined values (ex, <math>\ln(x)</math> at <math>x=0</math>) will cause a break when drawn in Asymptote (unlikely to be fixed); drawing the functions themselves will work, however.<br />
* With certain very contrived function strings, it is possible to break the code (won't fix).<br />
* Sometimes will render LaTeX commands in function strings. Please let me know if this happens.<br />
<br />
== Lines and Conics ==<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-5.06,xmax=6.54,ymin=-3.4,ymax=5.54; <br />
pen qqzztt=rgb(0,0.6,0.2), qqqqzz=rgb(0,0,0.6), ffqqtt=rgb(1,0,0.2);draw(circle((0,0),1),linewidth(2.8));draw((0,0)--(1,0)); draw((0,ymin)--(0,ymax)); draw((xmin,(-(3.19)-(1.03)*xmin)/3.02)--(xmax,(-(3.19)-(1.03)*xmax)/3.02)); draw((xmin,(-(-3.19)-(-0.88)*xmin)/3.06)--(xmax,(-(-3.19)-(-0.88)*xmax)/3.06)); draw(shift((-2.81,0.83))*rotate(54.75)*xscale(2.12)*yscale(1.91)*unitcircle,linewidth(1.6)+linetype("2pt 8pt 10pt 8pt")+qqzztt);pair hl1(real t){return (0.53*(1+t^2)/(1-t^2),0.74*2*t/(1-t^2));} pair hr1(real t){return (0.53*(-1-t^2)/(1-t^2),0.74*(-2)*t/(1-t^2));} draw(shift((3.63,0.55))*rotate(178.11)*graph(hl1,-0.99,0.99),linewidth(1.6)+linetype("4pt 4pt")+qqqqzz); draw(shift((3.63,0.55))*rotate(178.11)*graph(hr1,-0.99,0.99),linewidth(1.6)+linetype("4pt 4pt")+qqqqzz); real p1(real x){return x^2/2/3.48;} draw(shift((1.16,3.19))*rotate(16.04)*graph(p1,-13.93,13.93),linewidth(2)+ffqqtt); <br />
dot((0,0),ds); dot((1,0),ds); dot((-3.34,0.08),ds); dot((-2.28,1.58),ds); dot((-3.4,2.72),ds); dot((-0.94,0.34),ds); dot((2.72,0.58),ds); dot((4.54,0.52),ds); dot((0.68,4.86),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Allows lines, rays, vectors (not shown), and the different conic sections (which includes circle arcs and sectors), including different line colors, line types, line sizes, and in some cases, fill colors. Lines and rays automatically re-scale to fit the entire window when the diagram size is changed. <br />
<br />
<geogebra>f475aec9be4bbeb0d7a8b525fb2cbbe905383c5d</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Broken line functions (floor, ceiling) graph incorrectly. Not likely to be fixed due to Asymptote's graph() design.<br />
<br />
== Filled objects ==<br />
<asy><br />
import graph; size(9.7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.58,xmax=6.12,ymin=-1.1,ymax=6.1; <br />
pen cqcqcq=rgb(0.75,0.75,0.75), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0), evefev=rgb(0.9,0.94,0.9), qqwuqq=rgb(0,0.39,0);<br />
filldraw((0,0)--(2,0)--(3.41,1.41)--(3.41,3.41)--(2,4.83)--(0,4.83)--(-1.41,3.41)--(-1.41,1.41)--cycle,fueaev,zzttqq); filldraw(arc((2,0),0.6,45,180)--(2,0)--cycle,evefev,qqwuqq); filldraw(arc((0,0),0.6,0,135)--(0,0)--cycle,evefev,qqwuqq); filldraw(arc((-1.41,1.41),0.6,-45,90)--(-1.41,1.41)--cycle,evefev,qqwuqq); filldraw(arc((-1.41,3.41),0.6,-90,45)--(-1.41,3.41)--cycle,evefev,qqwuqq); filldraw(arc((0,4.83),0.6,-135,0)--(0,4.83)--cycle,evefev,qqwuqq); filldraw(arc((2,4.83),0.6,180,315)--(2,4.83)--cycle,evefev,qqwuqq); filldraw(arc((3.41,3.41),0.6,135,270)--(3.41,3.41)--cycle,evefev,qqwuqq); filldraw(arc((3.41,1.41),0.6,90,225)--(3.41,1.41)--cycle,evefev,qqwuqq); <br />
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2pt 2pt"); real gx=1,gy=1;<br />
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); draw((0,0)--(2,0),zzttqq); draw((2,0)--(3.41,1.41),zzttqq); draw((3.41,1.41)--(3.41,3.41),zzttqq); draw((3.41,3.41)--(2,4.83),zzttqq); draw((2,4.83)--(0,4.83),zzttqq); draw((0,4.83)--(-1.41,3.41),zzttqq); draw((-1.41,3.41)--(-1.41,1.41),zzttqq); draw((-1.41,1.41)--(0,0),zzttqq); draw(arc((2,0),0.6,0.79,pi),qqwuqq); draw(arc((2,0),0.5,0.79,pi),qqwuqq); draw(arc((-1.41,1.41),0.6,-45,85.38),qqwuqq,BeginArcArrow(6)); draw(arc((-1.41,3.41),0.6,-90,40.38),qqwuqq,EndArcArrow(6)); draw(arc((0,4.83),0.6,-2.36,0),qqwuqq); draw((0.21,4.33)--(0.25,4.22),qqwuqq); draw((0.14,4.31)--(0.17,4.19),qqwuqq); draw((0.27,4.36)--(0.33,4.26),qqwuqq); draw(arc((2,4.83),0.6,pi,5.5),qqwuqq); draw((1.73,4.36)--(1.67,4.26),qqwuqq); draw((1.86,4.31)--(1.83,4.19),qqwuqq); draw(arc((3.41,3.41),0.6,2.36,4.71),qqwuqq); draw((2.92,3.21)--(2.8,3.16),qqwuqq); draw(arc((3.41,1.41),0.6,1.57,3.93),qqwuqq); draw(arc((3.41,1.41),0.5,1.57,3.93),qqwuqq); draw(arc((3.41,1.41),0.4,1.57,3.93),qqwuqq); draw((0,0)--(2,0),EndArrow(6));<br />
dot((0,0),ds); dot((2,0),ds); dot((3.41,1.41),ds); dot((3.41,3.41),ds); dot((2,4.83),ds); dot((0,4.83),ds); dot((-1.41,3.41),ds); dot((-1.41,1.41),ds); label("$135^\circ$",(2.64,0.12),NE*lsf,qqwuqq); label("$135^\circ$",(0.28,0.78),NE*lsf,qqwuqq); label("$135^\circ$",(-1.1,2.06),NE*lsf,qqwuqq); label("$135^\circ$",(-0.72,3.28),NE*lsf,qqwuqq); label("$135^\circ$",(-1,4.68),NE*lsf,qqwuqq); label("$135^\circ$",(2.2,4.8),NE*lsf,qqwuqq); label("$135^\circ$",(3.38,3.64),NE*lsf,qqwuqq); label("$135^\circ$",(3.5,1.58),NE*lsf,qqwuqq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); </asy> Allows certain transparent fills. There are four possible options allowed for fill colors:<br />
<br />
* No fills. Self-explanatory.<br />
* Opaque fills only. This will only cause filled objects with opaque transparencies, which are arbitrarily defined as shapes with transparency alpha values greater than 0.9 (on a 0 to 1, 1 being fully opaque, scale), to appear filled.<br />
* With opacity pen. This uses the opacity() pen to draw transparency fills. This option does not work on the AoPS forums.<br />
* By layering (example above). Filled objects have "fake transparency" where filled objects are simply drawn before any other objects are drawn, and transparencies just cause a lighter shade. However, filled objects will override other filled objects, and so there is no "darker" transparencies along intersecting regions.<br />
<br />
Polygons and angles, by default, will have transparent fill colors. Both have support for different line colors and fill colors (with different transparencies, colors, line sizes, etc). Angles include several different styles, including multiple arcs, tick marks, and arc arrows. <br />
<geogebra>008edd5949bd2386cd1b9a7b223f16e44cbaf28c</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Non re-sized arc arrows. <br />
* Overlapping transparency colors do not sum together. <br />
<br />
== Text ==<br />
<asy><br />
import graph; size(11.58cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.3,xmax=7.28,ymin=-2.64,ymax=6.3; <br />
pen cqcqcq=rgb(0.75,0.75,0.75), qqccqq=rgb(0,0.8,0), ccqqtt=rgb(0.8,0,0.2);<br />
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("3pt 3pt"); real gx=1,gy=1;<br />
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); <br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis(-4.3,7.28,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); yaxis(-2.64,6.3,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); label("abc",(-3,5.24),SE*lsf); label("a2 b3 c3 o pi e infty otimes sqrt(x)",(-3,4.24),SE*lsf); label("$\parbox{1.4 cm}{abc \\ def \\ ghi}$",(-3,3.24),SE*lsf); label("$ \sqrt{ abc } $",(-3,2.24),SE*lsf); label("$abc \\ def$",(-3,1.24),SE*lsf); label("$abc$",(-3,0.24),SE*lsf); label("$\alpha\beta\gamma$",(-3,-0.76),SE*lsf); label("alpha beta gamma ",(-3,-1.76),SE*lsf); label("\textit{\textbf{abc}}",(0,5.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{\textbf{alpha beta gamma }}",(0,-1.76),SE*lsf,qqccqq+fontsize(12)); label("$\mathit{\mathbf{ \alpha\beta\gamma }}$",(0,-0.76),SE*lsf,ccqqtt+fontsize(12)); label("\textit{\textbf{$abc$}}",(0,0.24),SE*lsf,qqccqq+fontsize(12)); label("$\mathit{\mathbf{ abcdef }}$",(0,1.24),SE*lsf,ccqqtt+fontsize(12)); label("$\mathit{\mathbf{ \sqrt{ abc } }}$",(0,2.24),SE*lsf,ccqqtt+fontsize(12)); label("$\parbox{1.5 cm}{\textit{\textbf{abc \\ def \\ ghi}}}$",(0,3.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{\textbf{a2 b3 co pi e infty otimes sqrt(x)}}",(0,4.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{abc}",(3,5.24),SE*lsf,fontsize(8)); label("$\parbox{1.34 cm}{\textit{abc \\ def \\ ghi}}$",(3,3.24),SE*lsf,fontsize(8)); label("$\mathit{ \sqrt{ abc } }$",(3,2.24),SE*lsf,fontsize(8)); label("$\mathit{abcdef}$",(3,1.24),SE*lsf,fontsize(8)); label("\textit{$abc$}",(3,0.24),SE*lsf,fontsize(8)); label("\textit{alpha beta gamma }",(3,-1.76),SE*lsf,fontsize(8)); label("$\mathit{ \alpha\beta\gamma }$",(3,-0.76),SE*lsf,fontsize(8)); label("pi e infty otimes questeq ne le ge neg wedge vee parallel perp in subseteq subset cong equiv measuredangle triangle ",(3,4.24),SE*lsf); <br />
dot((-3,0),ds); dot((-3,1),ds); dot((-3,2),ds); dot((-3,3),ds); dot((-3,4),ds); dot((-3,5),ds); dot((0,5),ds); dot((0,4),ds); dot((0,3),ds); dot((0,2),ds); dot((0,1),ds); dot((0,0),ds); dot((0,-1),ds); dot((-3,-1),ds); dot((-3,-2),ds); dot((0,-2),ds); dot((3,5),ds); dot((3,4),ds); dot((3,3),ds); dot((3,2),ds); dot((3,1),ds); dot((3,0),ds); dot((3,-1),ds); dot((3,-2),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Supports most text options, including different font styles, bold, italics, and <math>\LaTeX</math>.<br />
<br />
<geogebra>087e142af582ed87e10a11362584f7ced9b606bd</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Including text strings with dollar signs will convert it to LaTeX. An odd number of dollar signs in a text string will usually cause an error (working on for <math>\LaTeX</math> strings).<br />
* Certain contrived strings will break the code (may never be fixed).<br />
* Fontsize might not be correct occasionally, especially for cse5 commands. (Please let me know if this happens.)<br />
<br />
<br />
== Locus construction ==<br />
<asy><br />
import graph; size(10.16cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-3.28,xmax=6.88,ymin=-2.9,ymax=4.3; <br />
pen xdxdff=rgb(0.49,0.49,1), uququq=rgb(0.25,0.25,0.25), ffqqtt=rgb(1,0,0.2);draw((1,ymin)--(1,ymax)); draw(circle((1,0),1.85));draw((xmin,(-(3.7)-(0)*xmin)/-2)--(xmax,(-(3.7)-(0)*xmax)/-2)); draw((1,(-(5.56)-(-3.19)*1)/1.28)--(xmax,(-(5.56)-(-3.19)*xmax)/1.28)); draw((2.48,ymin)--(2.48,ymax)); draw((xmin,(-(-17.1)-(0)*xmin)/12.76)--(xmax,(-(-17.1)-(0)*xmax)/12.76)); draw((2.48,1.34)--(2.43,1.37)--(2.38,1.4)--(2.33,1.43)--(2.28,1.46)--(2.23,1.49)--(2.17,1.51)--(2.08,1.56)--(1.98,1.61)--(1.88,1.65)--(1.79,1.69)--(1.69,1.73)--(1.6,1.76)--(1.5,1.78)--(1.41,1.81)--(1.32,1.82)--(1.23,1.84)--(1.14,1.85)--(1.05,1.85)--(0.96,1.85)--(0.87,1.85)--(0.77,1.84)--(0.68,1.82)--(0.59,1.81)--(0.5,1.78)--(0.41,1.76)--(0.31,1.73)--(0.22,1.69)--(0.12,1.65)--(0.03,1.61)--(-0.07,1.57)--(-0.17,1.51)--(-0.22,1.49)--(-0.27,1.46)--(-0.32,1.43)--(-0.37,1.4)--(-0.43,1.37)--(-0.48,1.34)--(-0.53,1.31)--(-0.59,1.28)--(-0.64,1.24)--(-0.69,1.21)--(-0.75,1.18)--(-0.81,1.14)--(-0.86,1.1)--(-0.92,1.07)--(-0.98,1.03)--(-1.04,0.99)--(-1.1,0.95)--(-1.16,0.91)--(-1.22,0.87)--(-1.28,0.83)--(-1.34,0.79)--(-1.41,0.75)--(-1.47,0.71)--(-1.54,0.67)--(-1.61,0.63)--(-1.67,0.58)--(-1.74,0.54)--(-1.81,0.5)--(-1.89,0.45)--(-1.96,0.41)--(-2.04,0.36)--(-2.11,0.32)--(-2.19,0.27)--(-2.27,0.23)--(-2.35,0.18)--(-2.44,0.14)--(-2.52,0.09)--(-2.61,0.05)--(-2.7,0)--(-2.79,-0.04)--(-2.89,-0.09)--(-2.98,-0.13)--(-3.08,-0.18)--(-3.13,-0.2)--(-3.18,-0.22)--(-3.24,-0.25)^^(6.81,-0.78)--(6.74,-0.76)--(6.66,-0.74)--(6.58,-0.72)--(6.51,-0.7)--(6.44,-0.68)--(6.37,-0.66)--(6.3,-0.64)--(6.23,-0.61)--(6.16,-0.59)--(6.1,-0.57)--(6.03,-0.55)--(5.97,-0.53)--(5.9,-0.51)--(5.84,-0.48)--(5.78,-0.46)--(5.72,-0.44)--(5.66,-0.42)--(5.6,-0.4)--(5.54,-0.37)--(5.49,-0.35)--(5.43,-0.33)--(5.38,-0.31)--(5.32,-0.28)--(5.27,-0.26)--(5.22,-0.24)--(5.17,-0.22)--(5.11,-0.19)--(5.06,-0.17)--(4.97,-0.13)--(4.87,-0.08)--(4.78,-0.04)--(4.73,-0.01)--(4.71,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.69,0)--(4.68,0.01)--(4.66,0.02)--(4.63,0.04)--(4.55,0.08)--(4.48,0.12)--(4.4,0.16)--(4.33,0.19)--(4.26,0.23)--(4.2,0.27)--(4.13,0.31)--(4.06,0.35)--(4,0.39)--(3.93,0.42)--(3.87,0.46)--(3.81,0.5)--(3.75,0.54)--(3.69,0.57)--(3.63,0.61)--(3.57,0.65)--(3.52,0.68)--(3.46,0.72)--(3.4,0.75)--(3.35,0.79)--(3.29,0.82)--(3.24,0.86)--(3.19,0.89)--(3.14,0.93)--(3.08,0.96)--(3.03,0.99)--(2.98,1.03)--(2.88,1.09)--(2.83,1.13)--(2.77,1.16)--(2.72,1.2)--(2.66,1.23)--(2.61,1.26)--(2.55,1.3)--(2.48,1.34),linewidth(2.8)+ffqqtt); <br />
dot((1,0),xdxdff); dot((1,2),blue); dot((-0.66,0.82),blue); dot((1,1.85),uququq); dot((2.28,1.34),xdxdff); dot((1,-1.85),uququq); dot((2.48,1.85),uququq); dot((2.48,1.34),uququq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Locus constructions with all of the usual lines options. Shown above is the "witch of aggensi". <br />
<br />
<geogebra>d2594993982afff858b6296678b2bab7bbe351d8</geogebra> <br />
<br />
Comment: Can create huge files. <br />
<br />
Known bugs: none.<br />
<br />
== Statistics ==<br />
<asy><br />
import graph; size(14.26cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(7); defaultpen(dps); pen ds=black; real xmin=-1.1,xmax=13.16,ymin=-2.36,ymax=6.58; <br />
pen ccffcc=rgb(0.8,1,0.8), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0);<br />
filldraw(box((0,0),(1,2)),fueaev,linewidth(2)+zzttqq); filldraw(box((1,0),(2,6)),fueaev,linewidth(2)+zzttqq); filldraw(box((2,0),(3,8)),fueaev,linewidth(2)+zzttqq); filldraw(box((3,0),(4,3)),fueaev,linewidth(2)+zzttqq); filldraw(box((4,0),(5,1)),fueaev,linewidth(2)+zzttqq); filldraw(box((3.5,-1.5),(8,-0.5)),fueaev,linewidth(2)+zzttqq); <br />
Label laxis; laxis.p=fontsize(7); <br />
xaxis(-1.1,13.16,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); draw((2,-1.5)--(2,-0.5),linewidth(2)+zzttqq); draw((9,-1.5)--(9,-0.5),linewidth(2)+zzttqq); draw((6,-1.5)--(6,-0.5),linewidth(2)+zzttqq); draw((2,-1)--(3.5,-1),linewidth(2)+zzttqq); draw((8,-1)--(9,-1),linewidth(2)+zzttqq); <br />
label("$b = 20$",(2.38,0.24),NE*lsf,zzttqq); label("$c = 6$",(6,-1.26),NE*lsf,zzttqq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); shipout(bbox(ccffcc,Fill)); <br />
</asy><br />
<br />
Does '''BoxPlot[], Histogram[]''' commands, as well as background colors.<br />
<br />
Known bugs: none known<br />
<br />
== Implicit functions ==<br />
Graph implicit functions that are polynomials in two variables <math>x,y</math> using Asymptote's <math>\texttt{contour}</math> package.<br />
<br />
See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=408683 here]. <br />
<br />
== Inequalities ==<br />
Graph a certain set of inequalities: functions, conics, and conjunction/disjunctions. (to do)<br />
<br />
== Full example ==<br />
<asy><br />
import graph; size(13.92cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-0.72,xmax=3.2,ymin=-1.81,ymax=1.35; <br />
pen ffqqcc=rgb(1,0,0.8), uququq=rgb(0.25,0.25,0.25), evefev=rgb(0.9,0.94,0.9), qqwuqq=rgb(0,0.39,0), evffff=rgb(0.9,1,1), qqffff=rgb(0,1,1);<br />
filldraw(arc((2.69,-1.5),0.16,134.59,180)--(2.69,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((2,-0.8),0.16,-113.2,-90)--(2,-0.8)--cycle,evefev,qqwuqq); filldraw(arc((2,-1.5),0.16,0,90)--(2,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((1.7,-1.5),0.16,0,66.8)--(1.7,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,157.5,180)--(1.31,0)--cycle,evefev,qqwuqq); filldraw(arc((0.38,0),0.16,0,90)--(0.38,0)--cycle,evefev,qqwuqq); filldraw(arc((2.23,0),0.16,90,180)--(2.23,0)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,0,22.5)--(1.31,0)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,22.5,112.5)--(1.31,0)--cycle,evffff,qqffff); filldraw(arc((0,0),0.16,0,45)--(0,0)--cycle,evffff,qqffff); draw((xmin,(-(0)-(0)*xmin)/1)--(xmax,(-(0)-(0)*xmax)/1)); draw(circle((0,0),1.31),linetype("4pt 4pt")+blue);draw(circle((1.31,0),1),linetype("4pt 4pt")+red);draw((0.92,0.92)--(0,0),linewidth(1.6)); draw((0,0)--(1.31,0),linewidth(1.6)); draw((0.92,0.92)--(1.31,0),linewidth(1.6)); draw((1.31,0)--(2.23,0.38),linewidth(1.6)); draw((2.23,0.38)--(0.92,0.92),linewidth(1.6)); draw((0.38,0.38)--(2.23,0.38),ffqqcc); draw((0,0)--(2.23,0.38),ffqqcc); draw((2.23,0.38)--(2.23,0),dotted); draw((0,0.38)--(0,0),dotted); draw((0,0.38)--(0.38,0.38),dotted); draw((0.38,0.38)--(0.38,0.38),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(0,0),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(1.31,0),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(1.31,0),linewidth(1.2)+linetype("1pt 1pt")); draw((2.69,-1.5)--(2,-0.8)); draw((2,-0.8)--(1.7,-1.5)); draw((1.7,-1.5)--(2.69,-1.5)); draw((2,-0.8)--(2,-1.5)); label("$r $",(2.69,-1.84),SE*lsf); label("r",(2.3,-1.39),SE*lsf); label("$ r\sqrt{ 2 } $",(2.75,-1.24),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(2.02,-1.85),SE*lsf); label("$45^\circ$",(2.41,-1.3),SE*lsf); label("$22.5^\circ$",(2.02,-0.96),SE*lsf); draw(circle((2.07,-1.43),0.01),qqwuqq); label("$90^\circ$",(2.15,-1.3),SE*lsf); label("$67.5^\circ$",(1.79,-1.28),SE*lsf); label("$22.5^\circ$",(0.84,0.1),SE*lsf); label("r",(0.71,-0.06),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(0.27,0.35),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.05,-0.12),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.09,0.63),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.44,0.31),SE*lsf); draw(circle((0.45,0.07),0.01),qqwuqq); label("$90^\circ$",(0.6,0.1),SE*lsf); draw(circle((2.16,0.07),0.01),qqwuqq); label("$90^\circ$",(2.31,0.17),SE*lsf); label("$22.5^\circ$",(1.64,0.11),SE*lsf); label("r",(2.04,-0.09),SE*lsf); draw((1.4,-0.2)--(1.11,0.17),EndArrow(6));label("$ \sqrt{ (r (\sqrt{ 2 } - 1) + r + r )^2 + (r (\sqrt{ 2 } - 1) )^2 }$",(1.58,-0.2),SE*lsf); label("$ = \sqrt{ (r (\sqrt{ 2 } + 1) )^2 + (r (\sqrt{ 2 } - 1) )^2 } $",(1.53,-0.37),SE*lsf); label("$\mathbf{=r \sqrt{ 6 }}$",(1.53,-0.72),SE*lsf,blue); label("$= \sqrt{ r^2 (3 + 2 \sqrt{ 2 }) + r^2 (3 - 2 \sqrt{ 2 }) } $",(1.53,-0.54),SE*lsf); label("$\mathbf{2r}$",(1.46,0.64),SE*lsf,blue); label("$\mathbf{\frac{BE}{AE} = \frac{r \sqrt{ 6 }}{2r} = \frac{ \sqrt{ 6 }}{2}}$",(0.78,-1.47),SE*lsf,red+fontsize(14)); draw((1.74,-1.13)--(0.83,-0.06),EndArrow(6));draw(circle((1.34,0.09),0.01),qqffff); label("$45^\circ$",(-0.01,0.13),SE*lsf); label("$90^\circ$",(-0.22,1.47),SE*lsf); label("$90^\circ$",(1.39,0.24),SE*lsf); draw((0.38,0)--(0.38,0.38),linewidth(0.4)+dotted); <br />
dot((0,0),blue); label("$B$",(-0.06,-0.09),NE*lsf,blue); dot((1.31,0),blue); label("$D$",(1.34,-0.09),NE*lsf,blue); dot((0.92,0.92),blue); label("$C$",(0.91,0.99),NE*lsf,blue); dot((2.23,0.38),blue); label("$E$",(2.27,0.39),NE*lsf,blue); dot((0.38,0.38),blue); label("$A$",(0.33,0.41),NE*lsf,blue); dot((0.38,0),linewidth(1pt)+uququq); label("$G$",(0.41,-0.1),NE*lsf,uququq); dot((0,0.38),linewidth(1pt)+uququq); dot((2.23,0),linewidth(1pt)+uququq); label("$F$",(2.24,-0.1),NE*lsf,uququq); dot((0.38,0.38),uququq); dot((1.7,-1.5),blue); dot((2,-0.8),blue); dot((2.69,-1.5),blue); dot((2,-1.5),blue); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy><br />
Courtesy of [[User:Kouichi Nakagawa]].<br />
<br />
<geogebra>9fa91fc57b9e5def39d73828270c8c027c565d85</geogebra></div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=User:Azjps/geogebra&diff=110384User:Azjps/geogebra2019-10-17T22:47:00Z<p>Vsar0406: /* Functions and Integrals */</p>
<hr />
<div>'''Gallery of examples''': The following [[Asymptote (Vector Graphics Language)|Asymptote]] codes were all generated from [[Geogebra]] files (File > Export > Graphics View as Asymptote ...). It is available in the current release of the Geogebra 4.0 Beta version. To download Geogebra 4.0, go [http://www.geogebra.org/forum/viewtopic.php?f=22&t=1387 here] and either choose the webstart (direct) version or choose one of the 3.9 version offline installers (as beta versions, there may unfixed bugs, although the versions are for the most part stable.)<br />
<br />
== Documentation ==<br />
Here is a fairly simple example that breaks down the contents of the output code, with Fill type set at "By layering".<br />
<br />
<asy><br />
/* Geogebra to Asymptote conversion, documentation at userscripts.org/scripts/show/72997 */<br />
import graph; size(14.26cm); <br />
real labelscalefactor = 0.5; /* changes label-to-point distance */<br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */<br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
<br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
Label laxis; laxis.p = fontsize(10); string xaxislabel (real x) {int n=round(x/pi); if(n==-1) return "$-\pi$"; if(n==1) return "$\pi$"; if(n==0) return "$0$"; return "$" + string(n) + "\pi$";} string yaxislabel (real x) {return "$" + string(x) + "\,\mathrm{}$";} <br />
xaxis("$x$",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */<br />
/* dots and labels */<br />
label("$f$",(-6.12,-0.12),NE * labelscalefactor); <br />
label("$a = 2$",(1.46,0.24),NE * labelscalefactor,zzttqq); <br />
dot((-3.14,0),dotstyle); <br />
label("$A$",(-3.06,0.12),NE * labelscalefactor); <br />
dot((2.2,2.04),dotstyle); <br />
dot((4.5,2.08),dotstyle); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
/* end of picture */<br />
</asy><br />
<br />
Here is the Asymptote code produced: (with some spacing added)<br />
<br />
<pre><br />
/* Geogebra to Asymptote conversion, documentation at userscripts.org/scripts/show/72997 */<br />
import graph; size(14.26cm); <br />
real labelscalefactor = 0.5; /* changes label-to-point distance */<br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */<br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
<br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
Label laxis; laxis.p = fontsize(10); <br />
string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} <br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
<br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} <br />
pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */<br />
<br />
/* dots and labels */<br />
label("<math>f</math>",(-6.12,-0.12),NE * labelscalefactor); <br />
label("<math>a = 2</math>",(1.46,0.24),NE * labelscalefactor,zzttqq); <br />
dot((-3.14,0),dotstyle); <br />
label("<math>A</math>",(-3.06,0.12),NE * labelscalefactor); <br />
dot((2.2,2.04),dotstyle); <br />
dot((4.5,2.08),dotstyle); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
/* end of picture */<br />
</pre><br />
<br />
Here is a line-by-line explanation: (<math>\texttt{/* COMMENT */}</math> are comments that are not read by the Asymptote engine.)<br />
<br />
<math>\texttt{import graph; size(14.26cm); }</math> are the opening commands: any files that need to be imported (in this case, [http://asymptote.sourceforge.net/doc/graph.html graph]), followed by the horizontal size in centimeters, as shown by the Export to Asymptote window. <br />
<br />
<math>\texttt{real labelscalefactor = 0.5; /* changes label-to-point distance */}</math> This variable scales the distance that labels are from their defined locations on the Geogebra window. This is due to an innate difference in the Asymptote and Geogebra treatment of labels: Geogebra positions labels with respect to a corner of the label, but Asymptote positions labels with respect to the center. Also, both have different default font sizes. The larger the value of <math>\texttt{labelscalefactor}</math>, the farther the Asymptote labels are dislocated from their respective points. Usually, <math>\texttt{labelscalefactor}</math> will have to be lowered to better position the labels (truer for longer labels). In concise mode, this variable is abbreviated as <math>\texttt{lsf}</math>.<br />
<br />
<pre><br />
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ <br />
pen dotstyle = black; /* point style */ <br />
</pre><br />
<br />
These are the definition of the default pens to use. <math>\texttt{dps}</math> stands for default pen style and produces the default pen style. <math>\texttt{dotstyle}</math> stands for the default dot style. In concise mode, the latter is abbreviated as <math>\texttt{ds}</math>, and in cse5, this option is completely replaced by the pen <math>\texttt{pointpen}</math>.<br />
<br />
<code>real xmin = -6.22,xmax = 8.04,ymin = -4.18,ymax = 4.76; /* image dimensions */ }</code><br />
<br />
As the comment suggests, these four variables define the boundaries of the picture (in the units of the picture). Rays and lines that go out of the picture are defined in terms of these variables, as well as the clip window. Thus, changing these variables should keep intact most of the Asymptote contents.<br />
<br />
<code><br />
pen fueaev = rgb(0.96,0.92,0.9); pen zzttqq = rgb(0.6,0.2,0); <br />
</code><br />
<br />
These pens are custom defined colors, which are actually defined by hexadecimal values of the associated colors. The colors can be changed in this line (changing a specific shade to a darker shade, for example). <br />
<br />
<code><br />
filldraw((-3.14,0)--(0,0)--(0,3.14)--(-3.14,pi )--cycle, fueaev, zzttqq); <br />
</code><br />
<br />
This <math>\texttt{filldraw}</math> command draws a square in the picture. Of note is that if the axes are defined in terms of pi, then some coordinates are defined in terms of the Asymptote variable <math>\texttt{pi}</math>. The command changes to <math>\texttt{draw}</math> if the Fill type is set to "None". <br />
<br />
<pre><br />
real f2 (real x) {return sin(x);} <br />
filldraw(graph(f2,0,pi )--(pi ,0)--(0,0)--cycle, fueaev, zzttqq); <br />
</pre><br />
<br />
Some commands have to be defined with respect to a function. <math>\texttt{f2}</math> returns the <math>\sin(x)</math> function, and the <math>\texttt{graph}</math> command draws <math>\texttt{f2}</math> from <math>x = 0</math> to <math>x = \pi</math>.<br />
<br />
<pre><br />
Label laxis; laxis.p = fontsize(10); <br />
string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} <br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
</pre><br />
<br />
These commands draw the axes. The <math>\texttt{laxis}</math> label specifies the label styles of the axes (e.g., the field <math>\texttt{laxis.p}</math> defines the desired font pen). <br />
<br />
The next line, the <pre>string xaxislabel (real x) {<br />
int n=round(x/pi); <br />
if(n==-1) return "<math>-\pi</math>"; <br />
if(n==1) return "<math>\pi</math>"; <br />
if(n==0) return "<math>0</math>"; <br />
return "<math>" + string(n) + "\pi</math>";} <br />
string yaxislabel (real x) {return "<math>" + string(x) + "\,\mathrm{}</math>";} </pre> are functions that define the labels for both axes. These are abbreviated as <math>\texttt{xlbl, ylbl}</math> in the concise mode. The first defines axes with labels with respect to <math>\pi</math>, and it formats the labels so that the <math>0</math> label simply outputs <math>0</math> instead of <math>0\pi</math>, and <math> \pm \pi</math> instead of <math> \pm 1\pi</math>. Finally, <br />
<br />
<pre><br />
xaxis("<math>x</math>",-6.22,8.04,Ticks(laxis,xaxislabel,Step=3.141592653589793,Size=2),Arrows(6),above=true); <br />
yaxis(-4.18,4.76,Ticks(laxis,yaxislabel,Step=1.0,Size=2),Arrows(6),above=true); <br />
</pre><br />
<br />
are the commands that actually construct the xaxis and the yaxis. For documentation, see [http://asymptote.sourceforge.net/doc/graph.html here].<br />
<br />
The next block of code does the actual construction of the geometric figures. <pre><br />
/* draw figures */<br />
real f1 (real x) {return sin(x);} <br />
draw(graph(f1,-6.21,8.03)); <br />
draw((-3.14,0)--(0,0), zzttqq); <br />
draw((0,0)--(0,3.14), zzttqq); <br />
draw((0,3.14)--(-3.14,pi ), zzttqq); <br />
draw((-3.14,pi )--(-3.14,0), zzttqq); <br />
draw(circle((0,3.14),1.14)); draw(shift((3.35,2.06))*rotate(1)*xscale(1.59)*yscale(1.1)*unitcircle); <br />
pair hyperbolaLeft1 (real t) {return (0.49*(1+t^2)/(1-t^2),1.04*2*t/(1-t^2));} pair hyperbolaRight1 (real t) {return (0.49*(-1-t^2)/(1-t^2),1.04*(-2)*t/(1-t^2));} <br />
draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaLeft1,-0.99,0.99)); draw(shift((3.35,2.06))*rotate(1)*graph(hyperbolaRight1,-0.99,0.99)); /* hyperbola construction */ </pre> The first line <tt>real f1 (real x) {return sin(x);} </tt> defines the <tt>sin()</tt> function to be drawn, and the next line <tt>draw(graph(f1,-6.21,8.03)); </tt> actually draws the graph to the diagram. The <tt>graph()</tt> command comes from the Asymptote <tt>graph</tt> [http://asymptote.sourceforge.net/doc/graph.html package]. The next few lines draw several line segments. The attribute <tt>zzttqq</tt> is a pen whose color is mapped from some rgb value (with conversions <tt>... 8 = y, 9 = z, a = a, b = b, ... </tt>).<br />
<br />
== Options ==<br />
An outline of the different available options. <br />
<br />
(The first three options are related and automatically update with respect to eath other).<br />
<br />
'''X/Y Units (cm)''': Indicates how many units in the picture correspond to 1 centimeter.<br />
<br />
'''Picture width/height''': Indicates what size the Asymptote output should be, in centimeters.<br />
<br />
'''xmin/xmax/ymin/ymax''': Indicates the dimensions of the picture in the picture's coordinates. <br />
<br />
(The next options change other features).<br />
<br />
'''Font size''': Changes the default font size. The value defaults at 10pt, but I personally recommend 7pt for any file with multiple text lines, which more closely approximates the size of the font in the Geogebra window. <br />
<br />
'''Fill type''': This includes four options as to how Geogebra elements with different fill colors should be implemented:<br />
<br />
* None: No fills are drawn.<br />
* Only opaque fills. This will only cause filled objects with opaque transparencies, which are arbitrarily defined as shapes with transparency alpha values greater than 0.9 (on a 0 to 1, 1 being fully opaque, scale), to appear filled.<br />
* With opacity pen. This uses the opacity() pen to draw transparency fills. This option does not work on the AoPS forums.<br />
* By layering (my personal preference). Filled objects have "fake transparency" where filled objects are simply drawn before any other objects are drawn, and transparencies just cause a lighter shade. However, filled objects will override other filled objects, and so there is no "darker" transparencies along intersecting regions.<br />
<br />
'''Concise code''': This produces shorter Asymptote code. Some of the changes between non-concise and concise code:<br />
<br />
* In non-concise code, most new commands have their own line. In concise code, there are at most about 8 lines of code. <br />
* Abbreviations are used for certain variables (labelscalefactor to lsf, xaxislabel to xlbl, gridx to gx, and so forth). <br />
* Pen colors are produced with a single line of pen declarations. <br />
* Functions are re-used where possible.<br />
* Less spacing. <br />
<br />
The advantages of concise code:<br />
<br />
* Less code to examine.<br />
* Non-concise code will usually not render on the AoPS forums due to size limits.<br />
* Guide to customizing code should be in the following posts.<br />
<br />
The disadvantages of concise code:<br />
<br />
* More difficult to read (especially without experience with my style of coding), exacerbated by lack of spacing.<br />
* No documentation comments.<br />
* Difficult to read through from given code window, requires wrap-around to read effectively.<br />
<br />
'''Concise with cse5''': There is also a cse5 option that allows the code to be further compactified with help with the cse5 package (see the stickies in this forum). <br />
<br />
* In non-concise code, most new commands have their own line. In cse5 code, there are at most about 8 lines of code. <br />
* Abbreviations are used for certain variables (labelscalefactor to lsf, xaxislabel to xlbl, gridx to gx, and so forth). <br />
* Pairs are given names and produced in a single line; color pens are also produced in a single line.<br />
* Functions are re-used where possible.<br />
* Command shortcuts, such as MP() and D() are used extensively.<br />
* Almost no spacing. <br />
<br />
The advantages of cse5 code:<br />
<br />
* Less code to examine.<br />
* With the exception of excessively complicated diagrams, will almost always fit within AoPS size restrictions.<br />
* Guide to customizing code should be in the following posts.<br />
* Allows more customization; changing a declared point and pen will reflect changes across the code. <br />
<br />
The disadvantages of cse5 code:<br />
<br />
* Extremely difficult to read (especially without experience with my style of coding), exacerbated by lack of spacing and short commands.<br />
* No documentation comments.<br />
* Difficult to read through from given code window, requires wrap-around to read effectively.<br />
* May occasionally draw skinny points and lines, due to default pathpen and pointpen attributes. <br />
<br />
My personal recommendation is the concise code for producing quick sketches (cse5 for large quick sketches), and the non-concise code otherwise.<br />
<br />
'''Grayscale''': Uses monochromatic scale to produce all output. <br />
<br />
'''Show Axes/Grid''' (default checked): Show or hide the axes and the grid.<br />
<br />
'''Keep dot colors''': Geogebra defaults free points to a blue color and semi-fixed points to a light blue color. Without this option checked, the Asymptote code will automatically set points to the default color (black). With checked, the Asymptote code will include the point colors as shown in the Geogebra window.<br />
<br />
'''Use point names''': (to do) In the Asymptote code, store points in <math>\texttt{pair}</math> variables rather than by write out by coordinates. Done by default for concise cse5 code.<br />
<br />
== Points ==<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-5.8,xmax=5.8,ymin=-2.2,ymax=5.72; <br />
pen wwqqqq=rgb(0.4,0,0), xdxdff=rgb(0.49,0.49,1), uququq=rgb(0.25,0.25,0.25), ffqqtt=rgb(1,0,0.2);<br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis("$x$",-5.8,5.8,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); yaxis("$y$",-3.22,5.72,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); draw(shift((-4,0))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),xdxdff); draw(circle((-3,0),0.11),xdxdff); draw(shift((-2,0))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0)),xdxdff); fill(shift((-1,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),xdxdff); draw(shift((0,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),uququq); fill(shift((1,0))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((2,0))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((3,0))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); fill(shift((4,0))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),xdxdff); draw(shift((-4,1))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),blue); draw(circle((-3,1),0.11),blue); draw(shift((-2,1))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0)),blue); fill(shift((-1,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),blue); draw(shift((0,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),xdxdff); fill(shift((1,1))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((2,1))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((3,1))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); fill(shift((4,1))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),blue); draw(shift((-4,2))*scale(0.18)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4)),ffqqtt); draw(circle((-3,2),0.18),ffqqtt); draw(shift((-2,2))*scale(0.18)*((0,1)--(0,-1)^^(1,0)--(-1,0)),ffqqtt); fill(shift((-1,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),ffqqtt); draw(shift((0,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle),ffqqtt); fill(shift((1,2))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((2,2))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((3,2))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); fill(shift((4,2))*rotate(180)*scale(0.25)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle),ffqqtt); <br />
dot((-5,0),xdxdff); label("$A$",(-4.92,0.12),NE*lsf,xdxdff); label("$B$",(-3.92,-0.12),NE*lsf,xdxdff); label("$C$",(-2.92,0.12),NE*lsf,xdxdff); label("$D$",(-1.92,0.12),NE*lsf,xdxdff); label("$E$",(-0.92,0.12),NE*lsf,xdxdff); label("$F$",(0.08,0.12),NE*lsf,uququq); label("$G$",(1.08,0.12),NE*lsf,xdxdff); label("$H$",(2.08,0.12),NE*lsf,xdxdff); label("$I$",(3.08,0.12),NE*lsf,xdxdff); label("$J$",(4.08,0.12),NE*lsf,xdxdff); dot((5,0),linewidth(1pt)+xdxdff); label("$K$",(5.08,0.04),NE*lsf,xdxdff); dot((-5,1),blue); label("$L$",(-4.92,1.12),NE*lsf,blue); label("$M$",(-3.92,1.12),NE*lsf,blue); label("$N$",(-2.92,1.12),NE*lsf,blue); label("$O$",(-1.92,1.12),NE*lsf,blue); label("$P$",(-0.92,1.12),NE*lsf,blue); label("$Q$",(0.08,1.12),NE*lsf,xdxdff); label("$R$",(1.08,1.12),NE*lsf,blue); label("$S$",(2.08,1.12),NE*lsf,blue); label("$T$",(3.08,1.12),NE*lsf,blue); label("$U$",(4.08,1.12),NE*lsf,blue); dot((5,1),blue); label("$V$",(5.08,1.12),NE*lsf,blue); dot((-5,2),blue); dot((5,2),linewidth(5pt)+blue); label("$I_1$",(5.08,2.2),NE*lsf,blue); dot((-5,3),blue); dot((-5,4),blue); dot((-5,3.5),uququq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> <br />
Support for drawing different options of points, along with point labeling. <br />
<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-5.8,xmax=5.8,ymin=-3.22,ymax=5.72; <br />
pen wwqqqq=rgb(0.4,0,0), ffqqtt=rgb(1,0,0.2);<br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis("$x$",-5.8,5.8,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); yaxis("$y$",-3.22,5.72,defaultpen+wwqqqq+linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),above=true); draw(shift((-4,0))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,0),0.11)); draw(shift((-2,0))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,0))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,0))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,0))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,0))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,0))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw(shift((-4,1))*scale(0.11)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,1),0.11)); draw(shift((-2,1))*scale(0.11)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,1))*scale(0.11)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,1))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,1))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,1))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,1))*rotate(180)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw(shift((-4,2))*scale(0.18)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); draw(circle((-3,2),0.18)); draw(shift((-2,2))*scale(0.18)*((0,1)--(0,-1)^^(1,0)--(-1,0))); fill(shift((-1,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); draw(shift((0,2))*scale(0.18)*((1,0)--(0,1)--(-1,0)--(0,-1)--cycle)); fill(shift((1,2))*rotate(90)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((2,2))*rotate(270)*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((3,2))*scale(0.11)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); fill(shift((4,2))*rotate(180)*scale(0.25)*((1,0)--expi(2*pi/3)--expi(4*pi/3)--cycle)); draw((-4,3)--(-4,4),ffqqtt); <br />
dot((-5,0),ds); label("$A$",(-4.92,0.12),NE*lsf); label("$B$",(-3.92,0.12),NE*lsf); label("$C$",(-2.92,0.12),NE*lsf); label("$D$",(-1.92,0.12),NE*lsf); label("$E$",(-0.92,0.12),NE*lsf); label("$F$",(0.08,0.12),NE*lsf); label("$G$",(1.08,0.12),NE*lsf); label("$H$",(2.08,0.12),NE*lsf); label("$I$",(3.08,0.12),NE*lsf); label("$J$",(4.08,0.12),NE*lsf); dot((5,0),linewidth(1pt)+ds); label("$K$",(5.08,0.04),NE*lsf); dot((-5,1),ds); label("$L$",(-4.92,1.12),NE*lsf); label("$M$",(-3.92,1.12),NE*lsf); label("$N$",(-2.92,1.12),NE*lsf); label("$O$",(-1.92,1.12),NE*lsf); label("$P$",(-0.92,1.12),NE*lsf); label("$Q$",(0.08,1.12),NE*lsf); label("$R$",(1.08,1.12),NE*lsf); label("$S$",(2.08,1.12),NE*lsf); label("$T$",(3.08,1.12),NE*lsf); label("$U$",(4.08,1.12),NE*lsf); dot((5,1),ds); label("$V$",(5.08,1.12),NE*lsf); dot((-5,2),ds); dot((5,2),linewidth(5pt)+ds); label("$I_1$",(5.08,2.2),NE*lsf); dot((-5,3),ds); dot((-5,4),ds); dot((-5,3.5),ds); dot((-4,3),ds); dot((-4,4),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Also includes an option to remove the coloring of just points (to avoid Geogebra's default of using different colors for different classes of fixed points). <br />
<br />
<br />
<geogebra>1c89b124bb471a351bc108d34f8096d1f892e012</geogebra> (Note, the version of Geogebra here does not support different dot styles.)<br />
<br />
<br />
Also has support for different types of axes: bold, with arrows, different colors, different labelling schemes (including with <math>\pi</math> labels as in the next example). Also supports drawing of grid (with for loop constructions). There is a checkbox option to show and hide axes and grids. <br />
<br />
Known bugs:<br />
<br />
* Labels may be displaced more from points than shown in Geogebra window. This is not really a bug but a font problem, since Asymptote will write the labels in LaTeX, which has a different size from normal text. The recommended solution is to decrease the font size to fontsize(8) or fontsize(7).<br />
* Leaving <b>Keep Dot Colors()</b> unchecked will color as black any labels which are a single character long and set to the default shade of blue for new points (presumably all such labels will be dot labels, which is the desired behavior).<br />
* Some of the point styles might not be perfectly accurate when zoomed in. <br />
* In cse5 mode, certain dots will appear smaller (default pointpen nature of cse5, not fixing).<br />
<br />
=== Axes ===<br />
There is support for drawing the x and y axes of the diagram (indeed, without <b>Show Axes/Grid</b> unchecked, and assuming the axes are visible in the Geogebra window, then the axes will be drawn). However, there are several bugs:<br />
* The Asymptote code will remove the tick labels for <math>0</math>. One can undo this by removing the attribute <tt>NoZero</tt> for the <tt>xaxis(), yaxis()</tt> commands. The reason is that the zero labels are not positioned well in Asymptote (indeed, the Geogebra tick labels for <math>0</math>, or whatever the intersection point is, are shifted slightly)<br />
* The location where the label of the axes (typically "x" or "y") will by default appear in the first quadrant ("x" above the x-axis, "y" to the right of the y-axis). In Asymptote, the labels appear in the exact opposite locations ("x" below the x-axis, "y" to the left of the y-axis). Low priority bug which is unlikely to be fixed.<br />
* There is no (easy) support in Asymptote for having the x or y axes intersect at any point other than the origin. In GeoGebra, one can use the <b>Crossing at</b> textbox under Properties to change where the x-axis and y-axis intersects. <br />
* Geogebra recognizes near-multiples of <math>\pi</math> in axis tick distances; for example, if you enter an axis tick distance of <math>\pi/3 \approx 1.047\ldots</math>, Geogebra automatically renders it as <math>\pi</math> instead of <math>3.14\ldots</math>. There's no easy way to do it in Asymptote (if you do want to try and mimic the behavior, manually add a labelling function which checks to see if tick labels are sufficient close to an integer multiple of <math>\pi</math>. The code is too long to be worth included in general). Also, while <math>\pi/2</math> labels are implemented, <math>\pi/4</math> labels are soon to be introduced and have not been implemented.<br />
<br />
== Functions and Integrals ==<br />
<asy><br />
import graph; size(5.12cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-7.3,xmax=8.06,ymin=-1.44,ymax=5.2; <br />
pen ttqqzz=rgb(0.2,0,0.6), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0);<br />
real f2(real x){return 2+2*cos(2*x+pi);} filldraw(graph(f2,-6.28,-3.14)--(-3.14,0)--(-6.28,0)--cycle,fueaev,zzttqq); filldraw(box((-3.14,0),(-2.51,0)),fueaev,zzttqq); filldraw(box((-2.51,0),(-1.88,1.38)),fueaev,zzttqq); filldraw(box((-1.88,0),(-1.26,3.62)),fueaev,zzttqq); filldraw(box((-1.26,0),(-0.63,1.38)),fueaev,zzttqq); filldraw(box((-0.63,0),(0,0)),fueaev,zzttqq); filldraw(box((0,0),(0.63,1.38)),fueaev,zzttqq); filldraw(box((0.63,0),(1.26,3.62)),fueaev,zzttqq); filldraw(box((1.26,0),(1.88,4)),fueaev,zzttqq); filldraw(box((1.88,0),(2.51,3.62)),fueaev,zzttqq); filldraw(box((2.51,0),(pi,1.38)),fueaev,zzttqq); filldraw((pi,0)--(3.77,0)--(3.77,1.38)--(pi,0)--cycle,fueaev,zzttqq); filldraw((3.77,0)--(4.4,0)--(4.4,3.62)--(3.77,1.38)--cycle,fueaev,zzttqq); filldraw((4.4,0)--(5.03,0)--(5.03,3.62)--(4.4,3.62)--cycle,fueaev,zzttqq); filldraw((5.03,0)--(5.65,0)--(5.65,1.38)--(5.03,3.62)--cycle,fueaev,zzttqq); filldraw((5.65,0)--(6.28,0)--(6.28,0)--(5.65,1.38)--cycle,fueaev,zzttqq); <br />
Label laxis; laxis.p=fontsize(10); string xlbl(real x){int n=round(x/pi); if(n==-1) return "$-\pi$"; if(n==1) return "$\pi$"; if(n==0) return "$0$"; return "$"+string(round(x/pi))+"\pi$";} <br />
xaxis("$\theta$",-7.3,8.06,linewidth(1.2),Ticks(laxis,xlbl,Step=3.141592653589793,Size=2),Arrows(6),above=true); yaxis(-1.44,5.2,linewidth(1.2),Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); real f1(real x){return 2+2*cos(2*x+pi);} draw(graph(f1,-7.29,8.05),linewidth(1.6)+ttqqzz); label("$2 + 2 \cos(2x + \pi)$",(-7.14,4.1),NE*lsf,ttqqzz); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Allows most functions and can draw integrals and Riemman-like sums. Above, the function is given by <math>f(x) = 2+2\cos(2x)</math>; the four shaded regions are drawn using the commands '''Integral[f,-2pi,-pi], LowerSum[f,-pi,0,5], UpperSum[f,0,pi,5],''' and '''TrapezoidalSum[f,pi,2pi,5]'''. <br />
<geogebra>6636ccd3479762307d932c319db7ec1998236a4c</geogebra> <br />
<br />
Known bugs:<br />
* May capitalize certain functions (like trigonometric functions). Please let me know if this happens.<br />
* Certain functions recognized by Geogebra might not be recognized by Asymptote.<br />
* Integrals/Sums drawn over functions that reach undefined values (ex, <math>\ln(x)</math> at <math>x=0</math>) will cause a break when drawn in Asymptote (unlikely to be fixed); drawing the functions themselves will work, however.<br />
* With certain very contrived function strings, it is possible to break the code (won't fix).<br />
* Sometimes will render LaTeX commands in function strings. Please let me know if this happens.<br />
<br />
== Lines and Conics ==<br />
<asy><br />
import graph; size(11.6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-5.06,xmax=6.54,ymin=-3.4,ymax=5.54; <br />
pen qqzztt=rgb(0,0.6,0.2), qqqqzz=rgb(0,0,0.6), ffqqtt=rgb(1,0,0.2);draw(circle((0,0),1),linewidth(2.8));draw((0,0)--(1,0)); draw((0,ymin)--(0,ymax)); draw((xmin,(-(3.19)-(1.03)*xmin)/3.02)--(xmax,(-(3.19)-(1.03)*xmax)/3.02)); draw((xmin,(-(-3.19)-(-0.88)*xmin)/3.06)--(xmax,(-(-3.19)-(-0.88)*xmax)/3.06)); draw(shift((-2.81,0.83))*rotate(54.75)*xscale(2.12)*yscale(1.91)*unitcircle,linewidth(1.6)+linetype("2pt 8pt 10pt 8pt")+qqzztt);pair hl1(real t){return (0.53*(1+t^2)/(1-t^2),0.74*2*t/(1-t^2));} pair hr1(real t){return (0.53*(-1-t^2)/(1-t^2),0.74*(-2)*t/(1-t^2));} draw(shift((3.63,0.55))*rotate(178.11)*graph(hl1,-0.99,0.99),linewidth(1.6)+linetype("4pt 4pt")+qqqqzz); draw(shift((3.63,0.55))*rotate(178.11)*graph(hr1,-0.99,0.99),linewidth(1.6)+linetype("4pt 4pt")+qqqqzz); real p1(real x){return x^2/2/3.48;} draw(shift((1.16,3.19))*rotate(16.04)*graph(p1,-13.93,13.93),linewidth(2)+ffqqtt); <br />
dot((0,0),ds); dot((1,0),ds); dot((-3.34,0.08),ds); dot((-2.28,1.58),ds); dot((-3.4,2.72),ds); dot((-0.94,0.34),ds); dot((2.72,0.58),ds); dot((4.54,0.52),ds); dot((0.68,4.86),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Allows lines, rays, vectors (not shown), and the different conic sections (which includes circle arcs and sectors), including different line colors, line types, line sizes, and in some cases, fill colors. Lines and rays automatically re-scale to fit the entire window when the diagram size is changed. <br />
<br />
<geogebra>f475aec9be4bbeb0d7a8b525fb2cbbe905383c5d</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Broken line functions (floor, ceiling) graph incorrectly. Not likely to be fixed due to Asymptote's graph() design.<br />
<br />
== Filled objects ==<br />
<asy><br />
import graph; size(9.7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.58,xmax=6.12,ymin=-1.1,ymax=6.1; <br />
pen cqcqcq=rgb(0.75,0.75,0.75), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0), evefev=rgb(0.9,0.94,0.9), qqwuqq=rgb(0,0.39,0);<br />
filldraw((0,0)--(2,0)--(3.41,1.41)--(3.41,3.41)--(2,4.83)--(0,4.83)--(-1.41,3.41)--(-1.41,1.41)--cycle,fueaev,zzttqq); filldraw(arc((2,0),0.6,45,180)--(2,0)--cycle,evefev,qqwuqq); filldraw(arc((0,0),0.6,0,135)--(0,0)--cycle,evefev,qqwuqq); filldraw(arc((-1.41,1.41),0.6,-45,90)--(-1.41,1.41)--cycle,evefev,qqwuqq); filldraw(arc((-1.41,3.41),0.6,-90,45)--(-1.41,3.41)--cycle,evefev,qqwuqq); filldraw(arc((0,4.83),0.6,-135,0)--(0,4.83)--cycle,evefev,qqwuqq); filldraw(arc((2,4.83),0.6,180,315)--(2,4.83)--cycle,evefev,qqwuqq); filldraw(arc((3.41,3.41),0.6,135,270)--(3.41,3.41)--cycle,evefev,qqwuqq); filldraw(arc((3.41,1.41),0.6,90,225)--(3.41,1.41)--cycle,evefev,qqwuqq); <br />
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("2pt 2pt"); real gx=1,gy=1;<br />
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); draw((0,0)--(2,0),zzttqq); draw((2,0)--(3.41,1.41),zzttqq); draw((3.41,1.41)--(3.41,3.41),zzttqq); draw((3.41,3.41)--(2,4.83),zzttqq); draw((2,4.83)--(0,4.83),zzttqq); draw((0,4.83)--(-1.41,3.41),zzttqq); draw((-1.41,3.41)--(-1.41,1.41),zzttqq); draw((-1.41,1.41)--(0,0),zzttqq); draw(arc((2,0),0.6,0.79,pi),qqwuqq); draw(arc((2,0),0.5,0.79,pi),qqwuqq); draw(arc((-1.41,1.41),0.6,-45,85.38),qqwuqq,BeginArcArrow(6)); draw(arc((-1.41,3.41),0.6,-90,40.38),qqwuqq,EndArcArrow(6)); draw(arc((0,4.83),0.6,-2.36,0),qqwuqq); draw((0.21,4.33)--(0.25,4.22),qqwuqq); draw((0.14,4.31)--(0.17,4.19),qqwuqq); draw((0.27,4.36)--(0.33,4.26),qqwuqq); draw(arc((2,4.83),0.6,pi,5.5),qqwuqq); draw((1.73,4.36)--(1.67,4.26),qqwuqq); draw((1.86,4.31)--(1.83,4.19),qqwuqq); draw(arc((3.41,3.41),0.6,2.36,4.71),qqwuqq); draw((2.92,3.21)--(2.8,3.16),qqwuqq); draw(arc((3.41,1.41),0.6,1.57,3.93),qqwuqq); draw(arc((3.41,1.41),0.5,1.57,3.93),qqwuqq); draw(arc((3.41,1.41),0.4,1.57,3.93),qqwuqq); draw((0,0)--(2,0),EndArrow(6));<br />
dot((0,0),ds); dot((2,0),ds); dot((3.41,1.41),ds); dot((3.41,3.41),ds); dot((2,4.83),ds); dot((0,4.83),ds); dot((-1.41,3.41),ds); dot((-1.41,1.41),ds); label("$135^\circ$",(2.64,0.12),NE*lsf,qqwuqq); label("$135^\circ$",(0.28,0.78),NE*lsf,qqwuqq); label("$135^\circ$",(-1.1,2.06),NE*lsf,qqwuqq); label("$135^\circ$",(-0.72,3.28),NE*lsf,qqwuqq); label("$135^\circ$",(-1,4.68),NE*lsf,qqwuqq); label("$135^\circ$",(2.2,4.8),NE*lsf,qqwuqq); label("$135^\circ$",(3.38,3.64),NE*lsf,qqwuqq); label("$135^\circ$",(3.5,1.58),NE*lsf,qqwuqq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); </asy> Allows certain transparent fills. There are four possible options allowed for fill colors:<br />
<br />
* No fills. Self-explanatory.<br />
* Opaque fills only. This will only cause filled objects with opaque transparencies, which are arbitrarily defined as shapes with transparency alpha values greater than 0.9 (on a 0 to 1, 1 being fully opaque, scale), to appear filled.<br />
* With opacity pen. This uses the opacity() pen to draw transparency fills. This option does not work on the AoPS forums.<br />
* By layering (example above). Filled objects have "fake transparency" where filled objects are simply drawn before any other objects are drawn, and transparencies just cause a lighter shade. However, filled objects will override other filled objects, and so there is no "darker" transparencies along intersecting regions.<br />
<br />
Polygons and angles, by default, will have transparent fill colors. Both have support for different line colors and fill colors (with different transparencies, colors, line sizes, etc). Angles include several different styles, including multiple arcs, tick marks, and arc arrows. <br />
<geogebra>008edd5949bd2386cd1b9a7b223f16e44cbaf28c</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Non re-sized arc arrows. <br />
* Overlapping transparency colors do not sum together. <br />
<br />
== Text ==<br />
<asy><br />
import graph; size(11.58cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.3,xmax=7.28,ymin=-2.64,ymax=6.3; <br />
pen cqcqcq=rgb(0.75,0.75,0.75), qqccqq=rgb(0,0.8,0), ccqqtt=rgb(0.8,0,0.2);<br />
/*grid*/ pen gs=linewidth(0.7)+cqcqcq+linetype("3pt 3pt"); real gx=1,gy=1;<br />
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); <br />
Label laxis; laxis.p=fontsize(10); <br />
xaxis(-4.3,7.28,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); yaxis(-2.64,6.3,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); label("abc",(-3,5.24),SE*lsf); label("a2 b3 c3 o pi e infty otimes sqrt(x)",(-3,4.24),SE*lsf); label("$\parbox{1.4 cm}{abc \\ def \\ ghi}$",(-3,3.24),SE*lsf); label("$ \sqrt{ abc } $",(-3,2.24),SE*lsf); label("$abc \\ def$",(-3,1.24),SE*lsf); label("$abc$",(-3,0.24),SE*lsf); label("$\alpha\beta\gamma$",(-3,-0.76),SE*lsf); label("alpha beta gamma ",(-3,-1.76),SE*lsf); label("\textit{\textbf{abc}}",(0,5.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{\textbf{alpha beta gamma }}",(0,-1.76),SE*lsf,qqccqq+fontsize(12)); label("$\mathit{\mathbf{ \alpha\beta\gamma }}$",(0,-0.76),SE*lsf,ccqqtt+fontsize(12)); label("\textit{\textbf{$abc$}}",(0,0.24),SE*lsf,qqccqq+fontsize(12)); label("$\mathit{\mathbf{ abcdef }}$",(0,1.24),SE*lsf,ccqqtt+fontsize(12)); label("$\mathit{\mathbf{ \sqrt{ abc } }}$",(0,2.24),SE*lsf,ccqqtt+fontsize(12)); label("$\parbox{1.5 cm}{\textit{\textbf{abc \\ def \\ ghi}}}$",(0,3.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{\textbf{a2 b3 co pi e infty otimes sqrt(x)}}",(0,4.24),SE*lsf,qqccqq+fontsize(12)); label("\textit{abc}",(3,5.24),SE*lsf,fontsize(8)); label("$\parbox{1.34 cm}{\textit{abc \\ def \\ ghi}}$",(3,3.24),SE*lsf,fontsize(8)); label("$\mathit{ \sqrt{ abc } }$",(3,2.24),SE*lsf,fontsize(8)); label("$\mathit{abcdef}$",(3,1.24),SE*lsf,fontsize(8)); label("\textit{$abc$}",(3,0.24),SE*lsf,fontsize(8)); label("\textit{alpha beta gamma }",(3,-1.76),SE*lsf,fontsize(8)); label("$\mathit{ \alpha\beta\gamma }$",(3,-0.76),SE*lsf,fontsize(8)); label("pi e infty otimes questeq ne le ge neg wedge vee parallel perp in subseteq subset cong equiv measuredangle triangle ",(3,4.24),SE*lsf); <br />
dot((-3,0),ds); dot((-3,1),ds); dot((-3,2),ds); dot((-3,3),ds); dot((-3,4),ds); dot((-3,5),ds); dot((0,5),ds); dot((0,4),ds); dot((0,3),ds); dot((0,2),ds); dot((0,1),ds); dot((0,0),ds); dot((0,-1),ds); dot((-3,-1),ds); dot((-3,-2),ds); dot((0,-2),ds); dot((3,5),ds); dot((3,4),ds); dot((3,3),ds); dot((3,2),ds); dot((3,1),ds); dot((3,0),ds); dot((3,-1),ds); dot((3,-2),ds); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Supports most text options, including different font styles, bold, italics, and <math>\LaTeX</math>.<br />
<br />
<geogebra>087e142af582ed87e10a11362584f7ced9b606bd</geogebra> <br />
<br />
Known bugs:<br />
<br />
* Including text strings with dollar signs will convert it to LaTeX. An odd number of dollar signs in a text string will usually cause an error (working on for <math>\LaTeX</math> strings).<br />
* Certain contrived strings will break the code (may never be fixed).<br />
* Fontsize might not be correct occasionally, especially for cse5 commands. (Please let me know if this happens.)<br />
<br />
<br />
== Locus construction ==<br />
<asy><br />
import graph; size(10.16cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-3.28,xmax=6.88,ymin=-2.9,ymax=4.3; <br />
pen xdxdff=rgb(0.49,0.49,1), uququq=rgb(0.25,0.25,0.25), ffqqtt=rgb(1,0,0.2);draw((1,ymin)--(1,ymax)); draw(circle((1,0),1.85));draw((xmin,(-(3.7)-(0)*xmin)/-2)--(xmax,(-(3.7)-(0)*xmax)/-2)); draw((1,(-(5.56)-(-3.19)*1)/1.28)--(xmax,(-(5.56)-(-3.19)*xmax)/1.28)); draw((2.48,ymin)--(2.48,ymax)); draw((xmin,(-(-17.1)-(0)*xmin)/12.76)--(xmax,(-(-17.1)-(0)*xmax)/12.76)); draw((2.48,1.34)--(2.43,1.37)--(2.38,1.4)--(2.33,1.43)--(2.28,1.46)--(2.23,1.49)--(2.17,1.51)--(2.08,1.56)--(1.98,1.61)--(1.88,1.65)--(1.79,1.69)--(1.69,1.73)--(1.6,1.76)--(1.5,1.78)--(1.41,1.81)--(1.32,1.82)--(1.23,1.84)--(1.14,1.85)--(1.05,1.85)--(0.96,1.85)--(0.87,1.85)--(0.77,1.84)--(0.68,1.82)--(0.59,1.81)--(0.5,1.78)--(0.41,1.76)--(0.31,1.73)--(0.22,1.69)--(0.12,1.65)--(0.03,1.61)--(-0.07,1.57)--(-0.17,1.51)--(-0.22,1.49)--(-0.27,1.46)--(-0.32,1.43)--(-0.37,1.4)--(-0.43,1.37)--(-0.48,1.34)--(-0.53,1.31)--(-0.59,1.28)--(-0.64,1.24)--(-0.69,1.21)--(-0.75,1.18)--(-0.81,1.14)--(-0.86,1.1)--(-0.92,1.07)--(-0.98,1.03)--(-1.04,0.99)--(-1.1,0.95)--(-1.16,0.91)--(-1.22,0.87)--(-1.28,0.83)--(-1.34,0.79)--(-1.41,0.75)--(-1.47,0.71)--(-1.54,0.67)--(-1.61,0.63)--(-1.67,0.58)--(-1.74,0.54)--(-1.81,0.5)--(-1.89,0.45)--(-1.96,0.41)--(-2.04,0.36)--(-2.11,0.32)--(-2.19,0.27)--(-2.27,0.23)--(-2.35,0.18)--(-2.44,0.14)--(-2.52,0.09)--(-2.61,0.05)--(-2.7,0)--(-2.79,-0.04)--(-2.89,-0.09)--(-2.98,-0.13)--(-3.08,-0.18)--(-3.13,-0.2)--(-3.18,-0.22)--(-3.24,-0.25)^^(6.81,-0.78)--(6.74,-0.76)--(6.66,-0.74)--(6.58,-0.72)--(6.51,-0.7)--(6.44,-0.68)--(6.37,-0.66)--(6.3,-0.64)--(6.23,-0.61)--(6.16,-0.59)--(6.1,-0.57)--(6.03,-0.55)--(5.97,-0.53)--(5.9,-0.51)--(5.84,-0.48)--(5.78,-0.46)--(5.72,-0.44)--(5.66,-0.42)--(5.6,-0.4)--(5.54,-0.37)--(5.49,-0.35)--(5.43,-0.33)--(5.38,-0.31)--(5.32,-0.28)--(5.27,-0.26)--(5.22,-0.24)--(5.17,-0.22)--(5.11,-0.19)--(5.06,-0.17)--(4.97,-0.13)--(4.87,-0.08)--(4.78,-0.04)--(4.73,-0.01)--(4.71,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.7,0)--(4.69,0)--(4.68,0.01)--(4.66,0.02)--(4.63,0.04)--(4.55,0.08)--(4.48,0.12)--(4.4,0.16)--(4.33,0.19)--(4.26,0.23)--(4.2,0.27)--(4.13,0.31)--(4.06,0.35)--(4,0.39)--(3.93,0.42)--(3.87,0.46)--(3.81,0.5)--(3.75,0.54)--(3.69,0.57)--(3.63,0.61)--(3.57,0.65)--(3.52,0.68)--(3.46,0.72)--(3.4,0.75)--(3.35,0.79)--(3.29,0.82)--(3.24,0.86)--(3.19,0.89)--(3.14,0.93)--(3.08,0.96)--(3.03,0.99)--(2.98,1.03)--(2.88,1.09)--(2.83,1.13)--(2.77,1.16)--(2.72,1.2)--(2.66,1.23)--(2.61,1.26)--(2.55,1.3)--(2.48,1.34),linewidth(2.8)+ffqqtt); <br />
dot((1,0),xdxdff); dot((1,2),blue); dot((-0.66,0.82),blue); dot((1,1.85),uququq); dot((2.28,1.34),xdxdff); dot((1,-1.85),uququq); dot((2.48,1.85),uququq); dot((2.48,1.34),uququq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy> Locus constructions with all of the usual lines options. Shown above is the "witch of aggensi". <br />
<br />
<geogebra>d2594993982afff858b6296678b2bab7bbe351d8</geogebra> <br />
<br />
Comment: Can create huge files. <br />
<br />
Known bugs: none.<br />
<br />
== Statistics ==<br />
<asy><br />
import graph; size(14.26cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(7); defaultpen(dps); pen ds=black; real xmin=-1.1,xmax=13.16,ymin=-2.36,ymax=6.58; <br />
pen ccffcc=rgb(0.8,1,0.8), fueaev=rgb(0.96,0.92,0.9), zzttqq=rgb(0.6,0.2,0);<br />
filldraw(box((0,0),(1,2)),fueaev,linewidth(2)+zzttqq); filldraw(box((1,0),(2,6)),fueaev,linewidth(2)+zzttqq); filldraw(box((2,0),(3,8)),fueaev,linewidth(2)+zzttqq); filldraw(box((3,0),(4,3)),fueaev,linewidth(2)+zzttqq); filldraw(box((4,0),(5,1)),fueaev,linewidth(2)+zzttqq); filldraw(box((3.5,-1.5),(8,-0.5)),fueaev,linewidth(2)+zzttqq); <br />
Label laxis; laxis.p=fontsize(7); <br />
xaxis(-1.1,13.16,defaultpen+black,Ticks(laxis,Step=1.0,Size=2),Arrows(6),above=true); draw((2,-1.5)--(2,-0.5),linewidth(2)+zzttqq); draw((9,-1.5)--(9,-0.5),linewidth(2)+zzttqq); draw((6,-1.5)--(6,-0.5),linewidth(2)+zzttqq); draw((2,-1)--(3.5,-1),linewidth(2)+zzttqq); draw((8,-1)--(9,-1),linewidth(2)+zzttqq); <br />
label("$b = 20$",(2.38,0.24),NE*lsf,zzttqq); label("$c = 6$",(6,-1.26),NE*lsf,zzttqq); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); shipout(bbox(ccffcc,Fill)); <br />
</asy><br />
<br />
Does '''BoxPlot[], Histogram[]''' commands, as well as background colors.<br />
<br />
Known bugs: none known<br />
<br />
== Implicit functions ==<br />
Graph implicit functions that are polynomials in two variables <math>x,y</math> using Asymptote's <math>\texttt{contour}</math> package.<br />
<br />
See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=408683 here]. <br />
<br />
== Inequalities ==<br />
Graph a certain set of inequalities: functions, conics, and conjunction/disjunctions. (to do)<br />
<br />
== Full example ==<br />
<asy><br />
import graph; size(13.92cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); real xmin=-0.72,xmax=3.2,ymin=-1.81,ymax=1.35; <br />
pen ffqqcc=rgb(1,0,0.8), uququq=rgb(0.25,0.25,0.25), evefev=rgb(0.9,0.94,0.9), qqwuqq=rgb(0,0.39,0), evffff=rgb(0.9,1,1), qqffff=rgb(0,1,1);<br />
filldraw(arc((2.69,-1.5),0.16,134.59,180)--(2.69,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((2,-0.8),0.16,-113.2,-90)--(2,-0.8)--cycle,evefev,qqwuqq); filldraw(arc((2,-1.5),0.16,0,90)--(2,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((1.7,-1.5),0.16,0,66.8)--(1.7,-1.5)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,157.5,180)--(1.31,0)--cycle,evefev,qqwuqq); filldraw(arc((0.38,0),0.16,0,90)--(0.38,0)--cycle,evefev,qqwuqq); filldraw(arc((2.23,0),0.16,90,180)--(2.23,0)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,0,22.5)--(1.31,0)--cycle,evefev,qqwuqq); filldraw(arc((1.31,0),0.16,22.5,112.5)--(1.31,0)--cycle,evffff,qqffff); filldraw(arc((0,0),0.16,0,45)--(0,0)--cycle,evffff,qqffff); draw((xmin,(-(0)-(0)*xmin)/1)--(xmax,(-(0)-(0)*xmax)/1)); draw(circle((0,0),1.31),linetype("4pt 4pt")+blue);draw(circle((1.31,0),1),linetype("4pt 4pt")+red);draw((0.92,0.92)--(0,0),linewidth(1.6)); draw((0,0)--(1.31,0),linewidth(1.6)); draw((0.92,0.92)--(1.31,0),linewidth(1.6)); draw((1.31,0)--(2.23,0.38),linewidth(1.6)); draw((2.23,0.38)--(0.92,0.92),linewidth(1.6)); draw((0.38,0.38)--(2.23,0.38),ffqqcc); draw((0,0)--(2.23,0.38),ffqqcc); draw((2.23,0.38)--(2.23,0),dotted); draw((0,0.38)--(0,0),dotted); draw((0,0.38)--(0.38,0.38),dotted); draw((0.38,0.38)--(0.38,0.38),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(0,0),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(1.31,0),linewidth(1.2)+linetype("1pt 1pt")); draw((0.38,0.38)--(1.31,0),linewidth(1.2)+linetype("1pt 1pt")); draw((2.69,-1.5)--(2,-0.8)); draw((2,-0.8)--(1.7,-1.5)); draw((1.7,-1.5)--(2.69,-1.5)); draw((2,-0.8)--(2,-1.5)); label("$r $",(2.69,-1.84),SE*lsf); label("r",(2.3,-1.39),SE*lsf); label("$ r\sqrt{ 2 } $",(2.75,-1.24),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(2.02,-1.85),SE*lsf); label("$45^\circ$",(2.41,-1.3),SE*lsf); label("$22.5^\circ$",(2.02,-0.96),SE*lsf); draw(circle((2.07,-1.43),0.01),qqwuqq); label("$90^\circ$",(2.15,-1.3),SE*lsf); label("$67.5^\circ$",(1.79,-1.28),SE*lsf); label("$22.5^\circ$",(0.84,0.1),SE*lsf); label("r",(0.71,-0.06),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(0.27,0.35),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.05,-0.12),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.09,0.63),SE*lsf); label("$r( \sqrt{ 2 } - 1 )$",(-0.44,0.31),SE*lsf); draw(circle((0.45,0.07),0.01),qqwuqq); label("$90^\circ$",(0.6,0.1),SE*lsf); draw(circle((2.16,0.07),0.01),qqwuqq); label("$90^\circ$",(2.31,0.17),SE*lsf); label("$22.5^\circ$",(1.64,0.11),SE*lsf); label("r",(2.04,-0.09),SE*lsf); draw((1.4,-0.2)--(1.11,0.17),EndArrow(6));label("$ \sqrt{ (r (\sqrt{ 2 } - 1) + r + r )^2 + (r (\sqrt{ 2 } - 1) )^2 }$",(1.58,-0.2),SE*lsf); label("$ = \sqrt{ (r (\sqrt{ 2 } + 1) )^2 + (r (\sqrt{ 2 } - 1) )^2 } $",(1.53,-0.37),SE*lsf); label("$\mathbf{=r \sqrt{ 6 }}$",(1.53,-0.72),SE*lsf,blue); label("$= \sqrt{ r^2 (3 + 2 \sqrt{ 2 }) + r^2 (3 - 2 \sqrt{ 2 }) } $",(1.53,-0.54),SE*lsf); label("$\mathbf{2r}$",(1.46,0.64),SE*lsf,blue); label("$\mathbf{\frac{BE}{AE} = \frac{r \sqrt{ 6 }}{2r} = \frac{ \sqrt{ 6 }}{2}}$",(0.78,-1.47),SE*lsf,red+fontsize(14)); draw((1.74,-1.13)--(0.83,-0.06),EndArrow(6));draw(circle((1.34,0.09),0.01),qqffff); label("$45^\circ$",(-0.01,0.13),SE*lsf); label("$90^\circ$",(-0.22,1.47),SE*lsf); label("$90^\circ$",(1.39,0.24),SE*lsf); draw((0.38,0)--(0.38,0.38),linewidth(0.4)+dotted); <br />
dot((0,0),blue); label("$B$",(-0.06,-0.09),NE*lsf,blue); dot((1.31,0),blue); label("$D$",(1.34,-0.09),NE*lsf,blue); dot((0.92,0.92),blue); label("$C$",(0.91,0.99),NE*lsf,blue); dot((2.23,0.38),blue); label("$E$",(2.27,0.39),NE*lsf,blue); dot((0.38,0.38),blue); label("$A$",(0.33,0.41),NE*lsf,blue); dot((0.38,0),linewidth(1pt)+uququq); label("$G$",(0.41,-0.1),NE*lsf,uququq); dot((0,0.38),linewidth(1pt)+uququq); dot((2.23,0),linewidth(1pt)+uququq); label("$F$",(2.24,-0.1),NE*lsf,uququq); dot((0.38,0.38),uququq); dot((1.7,-1.5),blue); dot((2,-0.8),blue); dot((2.69,-1.5),blue); dot((2,-1.5),blue); <br />
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); <br />
</asy><br />
Courtesy of [[User:Kouichi Nakagawa]].<br />
<br />
<geogebra>9fa91fc57b9e5def39d73828270c8c027c565d85</geogebra></div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=2004_AMC_10B_Problems/Problem_24&diff=1101612004 AMC 10B Problems/Problem 242019-10-07T02:46:25Z<p>Vsar0406: /* Solution 1 */</p>
<hr />
<div>In triangle <math>ABC</math> we have <math>AB=7</math>, <math>AC=8</math>, <math>BC=9</math>. Point <math>D</math> is on the circumscribed circle of the triangle so that <math>AD</math> bisects angle <math>BAC</math>. What is the value of <math>AD/CD</math>? <br />
<br />
<math>\text{(A) } \dfrac{9}{8} \quad \text{(B) } \dfrac{5}{3} \quad \text{(C) } 2 \quad \text{(D) } \dfrac{17}{7} \quad \text{(E) } \dfrac{5}{2}</math><br />
<br />
<br />
== Solution 1==<br />
<br />
Set <math>\overline{BD}</math>'s length as <math>x</math>. <math>\overline{CD}</math>'s length must also be <math>x</math> since <math>\angle BAD</math> and <math>\angle DAC</math> intercept arcs of equal length (because <math>\angle BAD=\angle DAC</math>). Using [[Ptolemy's Theorem]], <math>7x+8x=9(AD)</math>. The ratio is <math>\frac{5}{3}\implies\boxed{\text{(B)}}</math><br />
<br />
==Solution 2==<br />
<asy><br />
import graph;<br />
import geometry;<br />
import markers;<br />
<br />
unitsize(0.5 cm);<br />
<br />
pair A, B, C, D, E, I;<br />
<br />
A = (11/3,8*sqrt(5)/3);<br />
B = (0,0);<br />
C = (9,0);<br />
I = incenter(A,B,C);<br />
D = intersectionpoint(I--(I + 2*(I - A)), circumcircle(A,B,C));<br />
E = extension(A,D,B,C);<br />
<br />
draw(A--B--C--cycle);<br />
draw(circumcircle(A,B,C));<br />
draw(D--A);<br />
draw(D--B);<br />
draw(D--C);<br />
<br />
label("$A$", A, N);<br />
label("$B$", B, SW);<br />
label("$C$", C, SE);<br />
label("$D$", D, S);<br />
label("$E$", E, NE);<br />
<br />
markangle(radius = 20,B, A, C, marker(markinterval(2,stickframe(1,2mm),true)));<br />
markangle(radius = 20,B, C, D, marker(markinterval(1,stickframe(1,2mm),true)));<br />
markangle(radius = 20,D, B, C, marker(markinterval(1,stickframe(1,2mm),true)));<br />
markangle(radius = 20,C, B, A, marker(markinterval(1,stickframe(2,2mm),true)));<br />
markangle(radius = 20,C, D, A, marker(markinterval(1,stickframe(2,2mm),true)));<br />
</asy><br />
Let <math>E = \overline{BC}\cap \overline{AD}</math>. Observe that <math>\angle ABC \cong \angle ADC</math> because they subtend the same arc, <math>\overarc{AC}</math>. Furthermore, <math>\angle BAE \cong \angle EAC</math> because <math>\overline{AE}</math> is an angle bisector, so <math>\triangle ABE \sim \triangle ADC</math> by <math>\text{AA}</math> similarity. Then <math>\dfrac{AD}{AB} = \dfrac{CD}{BE}</math>. By the [[Angle Bisector Theorem]], <math>\dfrac{7}{BE} = \dfrac{8}{CE}</math>, so <math>\dfrac{7}{BE} = \dfrac{8}{9-BE}</math>. This in turn gives <math>BE = \frac{21}{5}</math>. Plugging this into the similarity proportion gives: <math>\dfrac{AD}{7} = \dfrac{CD}{\dfrac{21}{5}} \implies \dfrac{AD}{CD} = {\dfrac{5}{3}} = \boxed{\text{(B)}}</math>.<br />
<br />
== See Also ==<br />
<br />
{{AMC10 box|year=2004|ab=B|num-b=23|num-a=25}}<br />
{{MAA Notice}}</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Gmaas&diff=109417Gmaas2019-08-27T01:47:20Z<p>Vsar0406: </p>
<hr />
<div><br />
This is the holy bible of Gmaas for people who worship the Gmaas religion. This bible is available for anyone to read and edit, for that Gmaas is awesome due to the Gmaas' Biggest Theorem which Gmaas himself proved. This bible also contains facts about Gmaas, which are only for the eyes of Gmaas. Luckily, you are actually Gmaas, so feel free to look at the facts following the bible.<br />
<br />
-1. Gmaas once changed his profile image to a picture of gmmas<br />
<br />
0. THEM FACTS ABOUT THE GREAT EPIC AWESOME GMAAS: Words fail to describe the epic nature of Gmaas, for he is too almighty and powerful to be bound by the plebeian and trifling words. But even the Great Epic Awesome Plenipotentiary GMAAS cannot get rid of a language that's been around for a <math>100000000^{10000000000}</math> years and counting. That's older than he is.<br />
<br />
1. Gmaas' theorem states that for any math problem, Gmaas knows the answer to it. This theorem was proved by Gmaas.<br />
<br />
2. The GMATS were supposed to be called the GMAAS, but the manager, gmaas, wanted to eat some gnats. Gmaas has stopped eating gnats because they taste <s>bad</s> dreadful.<br />
<br />
3. Gmaas' archenemy is John Wick. John Wick once gave Gmaas 31,415,926,535,897,932,384,626,433,832,795,028,841,971,693,993,751,058,209,749,445,923,078,164,062,862,089,986,280,348,253,421,170,679 Oren Berries, but Gmaas thought they were Oran Berries. That is why Gmaas hates John Wick. Gmaas knew they were Oren Berries, because Gmaas knows everything, but he decided to play along. <br />
<br />
4. Gmaas wants every fact to have a pi reference. Gmaas created pi.<br />
<br />
5. Gmaas owned many memes. Then they died. He left the meme business because others took it over. Gmaas decided to make some more memes after that. Since then, he has been working for the government. All of the politicians are his henchmen. He controls the government. He wrote all of the laws and documents including the U.S. constitution. However, Gmaas doesn't believe in constitutions. He simply writes them for fun (or not, only gmaas knows!!!) <br />
<br />
6. Gmaas owns Scratch. Gmaas sued them because Scratch cat was supposed to be a picture of Gmaas. But this was one lawsuit he lost. Gmaas won that lawsuit, but he ate food so he calmed down and dropped the case. <br />
<br />
7. Thanos wishes he could be like Gmaas. It's why he got the Infinity Stones and snapped.<br />
<br />
8. Gmaas dies in Endgame, but he somehow possesses Thanos and kills everyone. Gmaas never dies. Gmaas has the power to die whenever he wants and frequently does this to escape others' woes in life. Of course, he himself never faces such troubles.<br />
<br />
9. He hates contemporary music. He only like Renaissance music, Baroque music, Classical music, and Romantic music. His only exception is Queen music(Especially Bohemian Rhapsody).Gmaas also likes Debussy. But he thinks rock'n'roll is awful.<br />
<br />
10. Gmaas is superior to you. If you see Gmaas or a picture of the Great Gmaas, bow down. It is proper to have a painting or lifesize sculpture of Gmaas. If you do not, Gmaas will put one of them there himself. EDIT EDIT: That is exactly why you should not have a statue of Gmaas: Gmaas will give you one for free. A life size sculpture of Gmaas will be infinitely large, because that is how superior Gmaas is. Pictures also have power, so pictures require power to make. Making a sculpture of Gmaas will require almost an infinite amount of power. Only Gmaas can make a quality sculpture of himself, and if anyone makes a low quality sculpture of Gmaas, it will be disrespectful to such a superior power. Therefore, it is best to let Gmaas make a proper sculpture of himself, so he is respected. If you want to respect him the most, you should have a high quality sculpture of Gmaas.<br />
<br />
11. Gmaas is known to barf entire universes at will. EDIT: Every once in a while, he barfs a furball, which always turns into a black hole. The less impressive ones turn into neutron stars.<br />
<br />
12. Gmaas farted and created a false vacuum, but then he burped, destroying the false vacuum.<br />
<br />
13. Gmaas was the first person to use the Infinity Gauntlet. EDIT: Gmaas created the Infinity Gauntlet and the Infinity Stones. EDIT EDIT: But Thanos stole them after Gmaas died for 0.31415926535 seconds.<br />
<br />
14. Gmaas killed Thanos with a swat of Gmaas's tail. Gmaas barfed and created a furball, which lead to a new dimension, where he put a newly revived Thanos to become a farmer, when Thor aimed for the head. Gmaas got mad and made him fat. EDIT: The presence of Gmaas killed Thanos.<br />
<br />
15. Gmaas won an infinite amount of games against AlphaGo and Gary Kasparov while eating dinner.<br />
<br />
16. Gmaas owns a pet: sseraj. Gmaas likes to play chess with his pets. EDIT: Gmaas has long moved on from chess because he was too good for it.<br />
<br />
17. Gmaas is so interesting that an entire science has been devoted to studying him: Gmaasology.<br />
<br />
18. Gmaas is the only known living being who has a PhD in Gmaasology.<br />
<br />
19. Most universities, including Harvard, are beginning to offer MAs in Gmaasology.<br />
<br />
20. Gmaasology is one of the most eminent fields of science, falling behind Physics, Biology, Chemistry, Economics, Geology, and Computer Programming.<br />
<br />
21. Gmaas wants his AoPS Wiki page to be the longest ever. EDIT: Sadly, the Gmaas page is only the fourth longest page on AoPS wiki. It has around 50,000 bytes. EDIT EDIT: The Gmaas page is getting closer and closer! Gmaas has beaten Primitive Pythagorean Triple and Proofs without words and is the second longest AoPS Wiki page. It now has around 60,000 bytes. However, it will still be a challenger to overcome 2008 iTest Problems, which has around 73,000 bytes. EDIT EDIT EDIT: Gmaas has beaten 2008 iTest Problems! It is the longest AoPS Wiki article ever. Gmaas's article has 89,119 bytes.<br />
<br />
22. Gmaas has the longest lifespan of any cat. He has lived for 3,141,592,653,589,793,238,462,643,383,279 years. (He is older than the universe.)<br />
<br />
23. Gmaas is the ancient Greek god of cats and catfish.<br />
<br />
24. Gmaas can turn things into gold. EDIT: Gmaas can turn anything into anything.<br />
<br />
25. Gmaas can eat lava. EDIT: Everyone can eat lava once. After you eat it once, you die. EDIT EDIT: Gmaas can eat anything.<br />
<br />
26. Gmaas's Theorem states that Gmaas knows the answer to any math problem. EDIT: That theorem was proved by Gmaas. EDIT EDIT: Gmaas's Theorem has real world applications: because Gmaas knows the answer to any math problem, you can use Gmaas to solve math problems. Gmaas is busy, so he charges a fee of one dollar for 1,000,000 math problems. EDIT EDIT EDIT: The fee has gone up. It is now 1,000,000 dollars for one math problem. Gmaas's technician made a mistake and reciprocaled the fee.<br />
<br />
27. Gmaas can only be described as Gmaas. EDIT: Gmaas has an age, but his age changes all the time. Every second his age increases by one second.<br />
<br />
28. Gmaas should be capitalized to show respect. EDIT: It is normal to capitalize people's names. EDIT EDIT: Gmaas isn't a person, he is a divine entity that takes the form of a cat, and should therefore be worshipped.<br />
<br />
29. The steps to summon Gmaas can be found at Talk:Gmaas.<br />
<br />
30. Gmaas owns your AoPS account 31.4159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912% of the time. EDIT: There is an exception to this: Gmaas owns his own account 99.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% of the time. The only time when Gmaas did not control his AoPS account was when he had slow internet. For Gmaas, "slow internet" happens when it takes more than a nanosecond to load a webpage. EDIT EDIT: Gmaas owns every AoPS account at some point. EDIT: You are actually controlled by Gmaas. So actually, Gmaas owns your AoPS account 100% of the time, and his AoPS account is owned by him 314% of the time. <br />
<br />
31. Everyone, except for me, is Gmaas. EDIT: You are also Gmaas. Gmaas is not me nor you. Gmaas is in us all and also not in us all. Why? The power of Gmaas. Gmaas is an energy field created by all living things. It surrounds us and penetrates us. It binds the galaxy together.<br />
<br />
32. Gmaas used to be a dog, but he didn't like to be a dog. So he became a cat.<br />
<br />
33. Gmaas can be spotted in The Matrix at 31:41:59, metric time.<br />
<br />
34. The Metropolitan Museum of Art and the Louvre are Gmaas's private art collections from 3:14 AM to 3:15 AM. EDIT: The only exception was on the 3141th day after its opening. EDIT EDIT: All the paintings in these museums are secretly portraits of Gmaas in his most glorious human/animal forms.<br />
<br />
35. Gmaas is a Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is blah blah blah blah blah blah blah blah blah blah blah blah blah blah.<br />
<br />
36. Gmaas says hello. EDIT: Gmaas does not speak; he only uses mind signals. Speaking is too primitive for Gmaas.<br />
<br />
37. For one day, Gmaas was Richard Rusczyk, Gmaas, and David Patrick at the same time. It felt strange, so Gmaas stopped.<br />
<br />
38. Gmaas, in addition to being the oldest cat in history, the most powerful cat in history, and the most confusing cat in history, is also the largest cat in history.<br />
<br />
39. Gmaas is dead--he was eaten for lunch. EDIT: The above sentence is incorrect. Gmaas has not sent a gamma ray burst to destroy the planet, which has happened every time someone has eaten Gmaas.<br />
<br />
40. Gmaas is the creator of the BCPI Ai project.<br />
<br />
41. Gmaas exists in <math>2\pi^2</math> dimensions because he doesn't like string theory.<br />
<br />
42. Christmas was actually supposed to be called Gmaasmas. Until it wasn't. EDIT: Christ is actually Gmaas. EDIT EDIT: Why? Because of the power of Gmaas.<br />
<br />
- <math>\pi</math> is a representation of how many pies Gmaas has eaten. EDIT: The number <math>\pi</math> was created by Gmaas. He took a ten-sided die and flipped it an infinite number of times. The numbers he rolled became the digits of <math>\pi</math>.<br />
<br />
- <math>e</math> is a representation of how many days Gmaas forgot to eat. EDIT: The number <math>e</math> was created by Gmaas. He took a book that has infinite pages and flipped to a random page. The digits of the page number became digits of <math>e</math>. EDIT EDIT: That is impossible. The previous fact would mean that <math>e</math> has a last digit, which it does not. EDIT EDIT EDIT: That is why Gmaas is still flipping to this day. EDIT EDIT EDIT EDIT: Why would he still be doing that? That would be boring. EDIT EDIT EDIT EDIT EDIT: Gmaas is not flipping the book now because he can flip an infinite amount of pages in <math>\frac{1}{\infty}</math> seconds. EDIT EDIT EDIT EDIT EDIT EDIT: Then why isn't he done? EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The power of Gmaas. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The editors of the Gmaas article like to make long chains of edits, don't we? : Yes, we do. : I do too. So do I. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The quantity of edits only verifies how high-quality this holy bible of Gmaas is, because with each edit, this bible becomes better. That is exactly why we are editing this. I will make one more edit, just to respect Gmaas.<br />
<br />
- Gmaas is the creator of everything including nothing. <br />
<br />
- According to recent DNA tests, famous historical people, such as Euclid, Julius Caesar, Omar Khayyam, George Washington, and Ramanujan are actually Gmaas in disguise. Gmaas has been thousands of people; only 99.9% of them were important historical figures. EDIT EDIT: They aren't dead. They're still alive. They are all dead reincarnations of Gmaas. Gmaas only has one reincarnation at a time. He is right now a cat living in sseraj's house. <br />
<br />
- Gmaas is a cat. EDIT: How many times do we say this? EDIT EDIT: Very many times. EDIT EDIT EDIT: Gmaas can be anything, but he chooses to be a cat. EDIT EDIT EDIT EDIT: He has been a human dozens of times. In fact, Gmaas painted the Lascaux cave paintings.<br />
<br />
- Gmaas has the following powers: trout, carp, earthworm, and catfish. Gmaas never uses any of them because Gmaas has an infinite number of powers. EDIT: Gmaas has used his catfish power several times. EDIT EDIT: Gmaas once used all his powers 3,141,592,653,589,793,238,462,643,383,279 times in 1 second.<br />
<br />
- Gmaas was once spotted in minecraft chewing a tree. EDIT: The tree broke. EDIT EDIT: Gmaas once broke a Nokia. EDIT EDIT EDIT: Gmaas can break anything except for Gmaas's logic. It is too strong. EDIT EDIT EDIT EDIT: Gmaas is strong.<br />
<br />
- Gmaas was spotted in Roblox eating a tacocat. EDIT: Tacocat is really just what happens when Gmaas sheds. Shedding is annoying for Gmaas, so he sheds no more. Therefore, there are only 271,828,182 tacocats in the world. EDIT EDIT: However, Tacocats reproduce, so they are not in danger of extinction.<br />
<br />
- Gmaas would like to go to Taco Bell, but Gmaas goes to Wendy's instead. No one knows why. EDIT: Because Taco Bell doesn't serve tacocats.<br />
<br />
- Gmaas real name is Grayson Maas. He is the CEO of AoPS. EDIT: Gmaas's real name is Gmaas. He is not the CEO of AoPS. EDIT EDIT: Gmaas has always been the master of AoPS as he is AoPS.<br />
<br />
- Gmaas has a pet pufferfish named Pafferfash. EDIT: He also has a goldfish named Sylgar.<br />
<br />
- Gmaas has colonized the universe. EDIT: Gmaas created the universe, so he is allowed to claim control over it. EDIT EDIT: Gmaas created every universe.<br />
<br />
- Some people think that Gmaas is a human. However, this has never been proven. Many AoPSers believe Gmaas is a cat. EDIT: Gmaas is a cat. EDIT EDIT: Yeah, we've said that already. EDIT EDIT EDIT: It does not matter how many times we say it; it will always be true. EDIT EDIT EDIT EDIT: Gmaas is a cat. EDIT EDIT EDIT EDIT EDIT: Right now he is a cat, but many of his lives have been other species. EDIT EDIT EDIT EDIT EDIT EDIT: He has been a dog, as said before, but it was too boring.<br />
<br />
- Gmaas started pastafarianism. But then converted to Catholicism because Gmaas knows all EDIT: In that religion, one can only eat pasta.<br />
<br />
- Gmaas could eat your hand, but he would not because hands taste bad.<br />
<br />
- According to the Interuniversal Gmaas Society, 17.548 percent of universe's population thinks that Gmaas is spelled "Gmass". EDIT: In case you don't know already, the name Gmass is spelled Gmaas. Alternative spellings include GMAAS, gmaas, gmaas, Gmaas, Gmail, Maas, G. Maas, G. Mass, Gabriel Maas, Genius of Maas, General Maas, Greek Mass, and the big fluffy kitty who lives in sseraj's house. These are no longer accepted spellings, and Gmaas is the current acceptable spelling.<br />
<br />
- The Interuniversal Gmaas Society was founded in 1314 on May 9th at 2:06:53 PM. EDIT: Ever since then, Gmaas day has been celebrated on May 9th.<br />
<br />
- The Interuniversal Gmaas Society has just reconstruct a lost book about Gmaas from Lucretius's De Rerum Natura. They researched this for three years. EDIT: A few years ago the Society compiled a biography of Gmaas's last twenty lives. EDIT EDIT: The only copies of these biographies are locked in the Gmaasian Library beneath the Library of Congress. EDIT EDIT EDIT: See the Gmaasology page for more information on these projects and others made by the Interuniversal Gmaas Society.<br />
<br />
- The Interuniversal Gmaas society has found out all of the information and more. For details on the history of the Interuniversal Gmaas Society, see the Gmaathamatics page.<br />
<br />
- Gmaas likes to surprise unsuspecting people.<br />
<br />
- Gmaas loves sparkly mechanical pencils. EDIT: Gmaas has eaten several mechanical pencils. EDIT EDIT: He absorbed them and became colorful for 0.271828182846 seconds.<br />
<br />
- This page is Gmaas's holy book where people go to worship Gmaas in Maas. EDIT: This is an unusual holy where everyone edits it. EDIT EDIT: That is the point. Gmaas is too lazy to write or to hire someone to write his own holy book, so he lets people write it for free. EDIT EDIT EDIT: Gmaas does not like being called lazy. Our language is simply too unimportant for him to waste time on.<br />
<br />
- Gmaas tastes like a furry meatball. EDIT: No one has ever tasted Gmaas's sacred body before. EDIT EDIT: Once, he was a catfish, and someone ate him for dinner. Gmaas was angry and the entire planet exploded. (This was on the planet Demeter. It blew up into so many pieces that the Asteroid Belt was formed. The biggest asteroid in the belt is called Ceres, the Roman version of Demeter, in honor of the lost planet.)<br />
<br />
- Gmaas's favorite food is pepperoni pizza. EDIT: Gmaas's favorite food is turnips. EDIT EDIT: Gmaas hates catnip and turnips, and pepperoni. He only likes alien alienish H2So4. EDIT EDIT EDIT: He does love turnips. He has a secret turnip garden under sseraj's house.<br />
<br />
- Gmaas is Johnny Johnny's Papa. EDIT: We'll never know. EDIT EDIT: Gmaas caught Johnny Johnny eating sugar and lying. He is Johnny Johnny's Papa.<br />
<br />
- Gmaas is in you, and Gmaas is in you, and Gmaas is in me. EDIT: Gmaas is in all cats. EDIT EDIT: He is not in every cat. The Guinness Book of World Records has a cat that does not have any Gmaas. EDIT EDIT EDIT: Gmaas invented The Guinness Book of World Records. EDIT EDIT EDIT EDIT: Gmaas invented the world. EDIT EDIT EDIT EDIT EDIT: Gmaas will also destroy the world.<br />
<br />
- Gmaas always remembers not to destroy the universe. EDIT: Once he forgot and had to travel back in time to stop it.<br />
<br />
- Gmaas created many user's accounts. EDIT: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058% of accounts on AoPS are Gmaas in disguise.<br />
<br />
- Gmaas is both living and nonliving. EDIT: He is living 90% of the time. Every once in a while he takes a break and dies.<br />
<br />
- Gmaas is quasiomnipotent. He cannot comprehend the stupidity of humans.<br />
<br />
- All hail the Gmaas cloud! EDIT: Gmaas is a cloud: a cloud of electrons and nuclei.<br />
<br />
- Some things are beyond possible human comprehension. Nothing is beyond Gmaas. EDIT: The only thing beyond Gmaas is his tail; he has never managed to eat it. EDIT EDIT: Once he ate it. It tasted bad, so he didn't ever eat it again.<br />
<br />
- Gmaas eats food and resides at King Arthur's throne when he feels like it. EDIT: King Arthur is dead. However, Welsh folk stories say that he will come back if the Welsh people are in trouble. EDIT EDIT: King Arthur lives on paper flour bags. He came back when the Welsh people didn't have enough bread.<br />
<br />
- Gmaas owns a rabbit. EDIT: Gmaas ate it on March 19, 2019. It reincarnated on the other side of the planet. EDIT EDIT: Gmaas ate it again on April 31, 2019.<br />
<br />
- Gmaas is both singular and plural. EDIT: It is usually singular. EDIT EDIT: The plural of Gmaas in English and in Latin is Gmaases. (Gmaas is a third declension noun: Gmaas, Gmaasis, m.)<br />
<br />
- Gmaas eats disbelievers as if they were donuts for breakfast. (Yet I'm somehow still alive. Do you think Gmaas actually ate my soul?) EDIT: Yes, I do. Gmaas is just typing through your account. EDIT EDIT: Gmaas typed through everyone's account. EDIT EDIT EDIT: Gmaas owns most AoPSers, including me. So that's why I'm typing.<br />
<br />
- Gmaas knows Jon Snow's parents. EDIT: Gmaas was Jon Snow's parents for 0.3141592653589793238 seconds, but it felt weird. So he became Gmaas again.<br />
<br />
- All Gmaas article editors will be escorted to Gmaas heaven after they die. EDIT: I hope so because I edited this article. EDIT EDIT: Me too.<br />
<br />
- Gmaas won all the wars. EDIT: He did not win the Intergmaasian War, which was between Gmaas's head and his tail. His tail won. Two flees died in the war. EDIT EDIT: Stefán Karl Stefansson died in the war, which made Gmaas very sad. Because of this, Gmaas<br />
started the world peace movement.<br />
<br />
- Gmail was named after Gmaas. EDIT: Google was named after Gmaas. EDIT EDIT: Almost every word starting with G is named after Gmaas.<br />
<br />
- Gmaas ate cat-food today. EDIT: Gmaas also ate it yesterday. EDIT EDIT: Only because there was no alien alienish H2So4.<br />
<br />
- Gmaas won Battle For Dream Island and Total Drama Island. EDIT: Gmaas made Dream Island. And he ate it. It tasted like dirt.<br />
<br />
- Somehow Gmaas exists at all places at the same time. EDIT: Gmaas does not exist in my kitchen. EDIT EDIT: I'll just go check. Aaaaaaaaah! He is in my kitchen. He is eating everything! He sees me! I am dyingiuhbjhjucbfwiknjfwvkjwfvnkfvw<br />
<br />
- Gmaas can lift with Gmaas's will. EDIT: Gmaas can lift with no one's will while he is sleepwalking.<br />
<br />
- Gmaas is the rightful heir to the Iron Throne. EDIT: Gmaas made the Iron Throne.<br />
<br />
- Gmaas is actually Teemo in League of Legends because Gmaas made LoL and they made a honorary Gmaas character.<br />
<br />
- Gmaas started the Game of Thrones. EDIT: Gmaas will end the Game of Thrones.<br />
<br />
- Gmaas has killed himself hundreds of times. He was reincarnated as a different species each time. EDIT: Gmaas has only died two times. Other times he was putting on a magic show. The kids were very impressed. EDIT EDIT: Gmaas has died and reincarnated thousands of times.<br />
<br />
- Gmaas created everything after puking. EDIT: He could not have puked because he is a god. Gods do not do that. EDIT EDIT: Gmaas does that. EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gordan's last name was named after Gmaas. EDIT: But Gmaas did not want people disrupting his beauty sleep. So he changed it.<br />
<br />
- Gmaas is more powerful than Gohan.<br />
<br />
- Gmaas is over 90000 years old. EDIT: Gmaas is trillions of years old.<br />
<br />
- Gmaas has 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 cat lives, maybe even more. Gmaas has 0 dog lives. EDIT: He has 314,159,265 fish lives. EDIT EDIT: Out of Gmaas's 314,159,265 fish lives, 271,828,182 are catfish lives. He has used up 141,421,356 of them. EDIT EDIT EDIT: Gmaas has infinitely lives of all types. EDIT EDIT EDIT EDIT: How? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Who wrote Harry Potter? None other than Gmaas himself. EDIT: That is incorrect. EDIT EDIT: The above post is irrelevant. Gmaas created J K Rowling. Therefore, he created Harry Potter. EDIT EDIT EDIT: Gmaas has strong logic. No one can break it. Not even Gmaas himself. He is still trying to this day.<br />
<br />
- Gmaas created the catfish. EDIT: See a few posts above for more information about Gmaas and catfish.<br />
<br />
- Gmaas has proven that the universe is infinite by traveling to the edge of the universe in a second. EDIT: He has never repeated this experiment because Gmaas is busy and has better things to do.<br />
<br />
- Gmaas founded Target, but then Gmaas sued them for making the mascot look like a dog when it was supposed to look like Gmaas. EDIT: They went broke because Gmaas sued them but then Gmaas ate a fudge popsicle that made him super hyper and he made Target not broke anymore in his hyperness.<br />
<br />
- Everyone has a bit of Gmaas inside them. EDIT: I don't. EDIT EDIT: Yes, you do.<br />
<br />
- Gmaas likes to eat popsicles. Especially the fudge ones that get him hyper. EDIT: Gmaas is a popsicle. EDIT EDIT: Then how come Gmaas hasn't melted? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- When Gmaas is hyper, he runs across Washington D.C. and grabs unsuspecting pedestrians, steals their phones, hacks into them, and downloads PubG onto their phone.<br />
<br />
- Gmaas's favorite cereal is fruit loops. Gmaas thinks it tastes like unicorns jumping on rainbows. EDIT: Gmaas eats unicorns jumping on rainbows like a toddler eats Goldfish.<br />
<br />
- Gmaas thinks that the McChicken has too much mayonnaise. EDIT: Gmaas thinks McDonald's is not good enough for him.<br />
<br />
- Gmaas is a champion pillow-fighter. EDIT: Gmaas invented pillows.<br />
<br />
- Gmaas colonized Mars. EDIT: Gmaas also colonized Jupiter, Pluto, and several other galaxies. Gmaas cloned little Gmaas robots (with Gmaas's amazingly robotic skill of coding) and put them all over a galaxy called Gmaasalaxy. EDIT EDIT: Gmaas has colonized the whole universe.<br />
<br />
- Gmaas has the ability to make every device play "The Duck Song" at will. EDIT: "The Duck Song" was copied off of the "Gmaas song," but the animators though Gmaas wasn't catchy enough.<br />
<br />
- Gmaas once caught the red dot and ate it. EDIT: Gmaas is a red dot.<br />
<br />
- Gmaas's favorite color is Gmaasian blue, a very rare blue that shines with the brightness of lightning. EDIT: it's <math>1000^1000x</math> brighter than lightning. Gmaasian blue occurs when a meteor hits the earth and usually is only seen for a few seconds. Only Gmaas has good enough eyesight to see it for that short a time. <br />
<br />
- Gmaas can create wormholes and false vacuums. EDIT: He is made out of exotic matter.<br />
<br />
- Gmaas is a champion pvp Minecraft player.<br />
<br />
- Gmaas doesn't like tacos. The last time he tried one he turned into a mouse and then caught himself.<br />
<br />
- Gmaas is the coach of True Ninja Music and Myth.<br />
<br />
- Gmaas caught a CP 6000 Mewtwo with a normal Pokeball in Pokemon Go.<br />
<br />
- Gmaas founded Costco.<br />
<br />
- Gmaas does not need to attend the FIFA World Cup. If Gmaas did, he would start the game with a goal and break the ankles of everyone watching the World Cup, including you, at the same time in a fraction of a second, even if you are watching from a device. EDIT: Gmaas created your device. EDIT EDIT: Gmaas is your device.<br />
<br />
- Gmaas can solve any puzzle instantly except for the 3x3 Rubik's Cube. EDIT: When Gmaas is handed a 3x3 Rubik's Cube, it is always already solved. Why? The power of Gmaas.<br />
<br />
- Gmaas caught a CP 20,000 Mewtwo with a normal Pokeball and no berries blindfolded first try in Pokemon Go.<br />
<br />
- When Gmaas flips coins, they always land tails, except when Gmaas makes bets with Zeus.<br />
<br />
- On Gmaas's math tests, Gmaas always gets <math>\infty</math>. EDIT: He gets a 26 on the AMC8 every year. The results never show him because Gmaas is no longer in middle school.<br />
<br />
- Gmaas's favorite number is <math>\pi</math>. It is also one of Gmaas's favorite foods. EDIT: Gmaas created <math>\pi</math>, as well as most other constants, such as <math>e</math> and <math>\sqrt{2}</math>.<br />
<br />
- Gmaas's burps created all gaseous planets.<br />
<br />
- Gmaas beat Luke Robatille in an epic showdown of catnip consumption.<br />
<br />
- Gmaas's wealth is unknown, but it is estimated to be more than Scrooge's. EDIT: It may be more than John D. Rockefeller. EDIT EDIT: More accurate estimates predict that Gmaas's wealth is infinite.<br />
<br />
- Gmaas has a summer house on Mars. EDIT: Gmaas has a fall house on Venus. EDIT EDIT: Gmaas has a winter house on Jupiter. EDIT EDIT EDIT: Gmaas has a spring house on Earth. EDIT EDIT EDIT EDIT: Gmaas also experiences a fifth season called wintrautumn. It happens during November and December and is the cross between fall and winter. Everything is dreary, but there is no snow. Gmaas spends wintrautumn in his house on Venus, where he is incinerated daily. He reincarnates every night through the power of Gmaas. EDIT EDIT EDIT EDIT EDIT: Gmaas invented a new season on Feb. 31, 2019 called wintrsummer. It is spring but transcends spring.<br />
<br />
- The Earth and all known planets are Gmaas's hairballs.<br />
<br />
- Gmaas attended Harvard, Yale, Stanford, MIT, UC Berkeley, Princeton, Columbia, and Caltech at the same time using a time-turner.<br />
<br />
- Gmaas attended Hogwarts and was a prefect. EDIT: Gmaas is headmaster. EDIT EDIT: Hogwarts was supposed to be called Hogmaas.<br />
<br />
- Mrs. Norris is Gmaas's archenemy. Gmaas yawned, and Ms. Norris was petrified. EDIT: Gmaas is the basilisk, and he let Harry Potter pet him. Harry did not kill the basilisk, he only gave Gmaas a haircut. EDIT EDIT: Gmaas hates having a haircuts, so he reincarnated Voldemort to punish Harry.<br />
<br />
- Gmaas is a demigod and attends Camp Half-Blood over summer. Gmaas is the counselor for the Apollo cabin because cats can be demigod counselors too. EDIT: Apollo was one of the many reincarnations of Gmaas.<br />
<br />
- Gmaas has completed over 2,000 quests and is very popular throughout Camp Half-Blood. Gmaas has also been to Camp Jupiter. EDIT: Gmaas is Camp Jupiter, he is also Camp Half-Blood. EDIT EDIT: How? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Percy Jackson was only able to complete his quests because Gmaas helped him. EDIT: Gmaas is Percy Jackson. In fact, you are Gmaas, but Gmaas is not you.<br />
<br />
- Gmaas painted the Mona Lisa, The Last Supper, and A Starry Night. EDIT: Gmaas knows that their real names are Gmaasa Lisa, The Last Domestic Meal, and Far-away Light.<br />
<br />
- Gmaas knows that the Blood Moon is just the red dot. He has not caught it yet. EDIT: He caught it during the super blue blood moon.<br />
<br />
- Gmaas attended all the Ivy Leagues.<br />
<br />
- I am Gmaas. EDIT: No you are not. You only have part of Gmaas inside of you. EDIT EDIT: I am also Gmaas. EDIT EDIT EDIT: But it is I who am Gmaas. EDIT EDIT EDIT EDIT: Gmaas is in us all. EDIT EDIT EDIT EDIT EDIT: Gmaas is all of us yet none of us. EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas is a cat. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: He is only in a cat form right now. He can be whatever he wants to be. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: This chain of edits has superseded another chain of edits on this page for the record of longest chain of edits on AoPS Wiki. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: But the edits in this chain tend to be shorter than most. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: You're right. But we sure do love strings of edits, don't we? EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas makes the edits. He is in your head spinning edits in your brain. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas is made to be edited. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas pays people to edit. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Some people edit even without Gmaas's payment. They do it because they are believers.<br />
<br />
- In 2018 Gmaas once challenged Magnus Carlsen to a chess game. Gmaas won every round. EDIT: Gmaas ate the chess pieces afterwards. They tasted funny.<br />
<br />
- Gmaas was captured in 2017 but was released due to sympathy. EDIT: Gmaas was only captured in his concrete form; his abstract form cannot be processed by a feeble human brain.<br />
<br />
- Gmaas's fur is white, black, grey, yellow, red, blue, green, brown, pink, orange, turquoise, and purple at the same time. EDIT: Gmaas can make his fur any color he wants. EDIT EDIT: Gmaas's fur color can be ultraviolet.<br />
<br />
- Gmaas crossed the event horizon of a black hole and ended up in the AoPS universe.<br />
<br />
- Gmaas crossed the Delaware River with Washington. EDIT: Gmaas also crossed the Atlantic with the pilgrims.<br />
<br />
- If you are able to capture a Gmaas hair, Gmaas will give you some of his Gmaas power. EDIT: Gmaas does not shed and will eat anyone who has Gmaas hair. EDIT EDIT: Gmaas used to shed. The sheddings became tacocats.<br />
<br />
- Chuck Norris makes Gmaas jokes. EDIT: Those jokes all praise Gmaas.<br />
<br />
- Gmaas is also the ruler of Oceania, Eastasia, and Eurasia. EDIT: Gmaas wrote the book "1984."<br />
<br />
- Gmaas killed Big Brother by farting on him. Though Gmaas was caught by the Ministry of Love, Gmaas escaped easily. EDIT: Gmaas used to be Big Brother. EDIT EDIT: Gmaas destroyed the Ministry of Love.<br />
<br />
- Gmaas was not affected by Thanos's snap; in fact Gmaas is the creator of the Infinity Stones. EDIT: Gmaas is Thanos.<br />
<br />
- Everyone knows that Gmaas is a god. EDIT: That is because he is a god.<br />
<br />
- Gmaas also owns Animal Farm. Napoleon was Gmaas's servant. EDIT: Napoleon was Gmaas's slave.<br />
<br />
- Gmaas is the only person who knows where Amelia Earhart is. EDIT: Gmaas! Please tell us! It would be a great contribution to historical knowledge! EDIT EDIT: Gmaas responds, "No."<br />
<br />
- Gmaas is the only cat that has been proven transcendental. EDIT: Gmaas has been proved to be normal as well.<br />
<br />
- Grumpy cat reads Gmaas memes. EDIT: Grumpy cat then steals them and claims they're his. Gmaas isn't very happy about that, either. EDIT EDIT: That is why he looks grumpy in the memes.<br />
<br />
- The reason why AIME cutoffs aren't out yet is that Gmaas refused to grade them due to too much problem misplacement. EDIT: Gmaas controls the MAA. EDIT EDIT: Gmaas founded the MAA. EDIT EDIT EDIT: Gmaas is the MAA.<br />
<br />
- Gmaas dueled Grumpy Cat and won. Gmaas wasn't trying. EDIT: Gmaas killed Grumpy cat. EDIT EDIT: Gmaas revived Grumpy cat because he has not other rival.<br />
<br />
- Gmaas sits on the statue of Pallas and says forevermore. EDIT: When Gmaas was a statue, people hid him in a basement and forgot about him. Then civilization collapsed and the Middle Ages began. People finally discovered and melted down the statue of Gmaas around 1350 to make a church bell. Gmaas was free and reincarnated again, bringing about the Renaissance. EDIT EDIT: Despite the efforts of the recently founded National Gmatthematical Society of Florence, the statue was melted down. For more information about the National Gmatthematical Society of Florence, see the Gmaasology page.<br />
<br />
- Gmaas is a big fan of Edgar Allan Poe because he is actually Poe. EDIT: He became Poe during his thirty-year depression in the 19th century.<br />
<br />
- Gmaas does merely not use USD; he owns it.<br />
<br />
- In 2003, Gmaas used elliptical curves to force his reign over AoPS.<br />
<br />
- "Actually, my name is spelled "GMAAS"." (Citation needed)<br />
<br />
- Gmaas is Link in the Legend of Zelda. He despises Calamity Ganon in Breath of the Wild. "Too much of a hog..."<br />
<br />
- Gmaas is the smartest living being in the universe. EDIT: Notice how this sentences says "living being," so Gmaas might be dummer than some dead person. EDIT EDIT: Gmaas is the smartest being that has lived, lives, and will live. EDIT EDIT EDIT: How? EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas helped Sun Wukong on the Journey to the West.<br />
<br />
- Gmaas was the creator of Wikipedia.<br />
<br />
- Gmaas can hack any website he desires. EDIT: He can edit any website with the words Gmaas in it. EDIT EDIT: AoPS includes the word Gmaas right here, so Gmaas can hack it. EDIT EDIT EDIT: Gmaas can edit any website he desires.<br />
<br />
- Gmaas is the basis of Greek and Egyptian mythology. EDIT: He is also the basis for Aztec mythology. He once had a craving for human flesh, so he created human sacrifice.<br />
<br />
- Gmaas once sold Google to a man for around 12 dollars! EDIT: Gmaas has not spent those 12 dollars and is waiting for the economy to crash. EDIT EDIT: Why would he do that? EDIT EDIT EDIT: The power of Gmaas. EDIT EDIT EDIT EDIT: Gmaas is smarter than you think he is. Do you think you know how smart Gmaas is now? If so, then you are still wrong.<br />
<br />
- Gmaas uses a HP printer. It is specifically a HP 21414144124124142141414412412414214141441241241421414144124124142141414412412414 printer.<br />
<br />
- Gmaas owns all AoPS staff including Richard Rusczyk. EDIT: Richard Rusczyk is one of Gmaas's many code names.<br />
<br />
- Gmaas saw Yoda's birth. EDIT: Gmaas was Yoda's father. EDIT EDIT: Was Gmaas green like Yoda back then? EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas's true number of lives left is unknown; however, Gmaas recently confirmed that he had at least one left. Why doesn't Gmaas have so many more lives than other cats? The power of Gmaas. EDIT: This is all not true. EDIT EDIT: This is all true. EDIT EDIT EDIT: Gmaas has an infinite number of lives. EDIT EDIT EDIT EDIT: Gmaas does not have an infinite number of lives. He just has an unlimited number of lives.<br />
<br />
- sseraj once spelled Gmaas as gmASS by accident in Introduction to Geometry (1532). sseraj’s life was never the same afterwards. EDIT: Gmaas created sseraj. He is a Gmaas, but without the face, body, legs, and tail.<br />
<br />
- Gmaas has beaten Chuck Norris, The Rock, and John Cena all together in a fight.<br />
<br />
- Gmaas is a South Korean, North Korean, Palestinian, Israeli, U.S., Soviet, Russian, and Chinese citizen at the same time. EDIT: Gmaas is a citizen of every country in the world. Gmaas seems to enjoy the country of AoPS best, however.<br />
<br />
- "I am sand" destroyed Gmaas in FTW. EDIT: Because Gmaas accidentally died, he defeated "I am sand" 3,141,592,653 times after.<br />
<br />
- sseraj posted a picture of Gmaas with a game controller in Introduction to Geometry (1532).<br />
<br />
- Gmaas plays Roblox mobile edition and likes Minecraft, Candy Crush, and Club Penguin Rewritten. He also loves Catch that fish.<br />
<br />
- Gmaas is Roy Moore's horse in the shape of a cat.<br />
<br />
- Gmaas is a known roblox/club penguin rewritten player and is a legend at it. He has over <math>289547987693</math> roblox and <math>190348</math> in CPR.<br />
<br />
- This is all hypothetical. EDIT: This is all factual. For reference, see an earlier post.<br />
<br />
- Gmaas's real name is Princess. He has a sibling named Rusty/Fireheart/Firestar. EDIT: That is incorrect. Gmaas's real name is Gmaas.<br />
<br />
- Gmaas is capable of salmon powers. EDIT: Gmaas is capable of everything. Nothing is beyond Gmaas.<br />
<br />
- Gmaas told Richard Rusczyk to make AoPS.<br />
<br />
- The Gmaas is everything. Yes, you are part of the Gmaas-Dw789. EDIT: Gmaas is older than the universe. He is more than everything.<br />
<br />
- The Gmaas knows every dimension up to 99999999999999999999999999999999999999999999999999999999999999999999999999999999999th dimension. EDIT: He is working on the higher dimensions presently. It takes up 1% of his time. He spends the remaining 99% of his time eating, sleeping, and being. EDIT EDIT: Does that mean he stops being while he learns higher dimensions? EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas went into a black hole and exited the white hole. He ended up in the 15th dimension where people drink tea every day. He stole 31,415,926,535,897,932,384,626,433,832,795,028,841,971,693,993,751,058,209,749,445,923,078,164,062,862,089,986,280,348,253,421,170,679,821,480,865,132,823,066,470,938,446,095,505,822,317,253,594,081,284,811,174,502,841,027,019,385,211,055,596,446,229,489,549,303,819,644,288,109,756,659,334,461,284,756,482,337,867,831,652,712,019,091,456,485,669,234,603,486,104,543,266,482,133,936,072,602,491,412,737,245,870,066,063,155,881,748,815,209,209,628,292,540,917,153,643,678,925,903,600,113,305,305,488,204,665,213,841,469,519,415,116,094,330,572,703,657,595,919,530,921,861,173,819,326,117,931,051,185,480,744,623,799,627,495,673,518,857,527,248,912,279,381,830,119,491,298,336,733,624,406,566,430,860,213,949,463,952,247,371,907,021,798,609,437,027,705,392,171,762,931,767,523,846,748,184,676,694,051,320,005,681,271,452,635,608,277,857,713,427,577,896,091,736,371,787,214,684,409,012,249,534,301,465,495,853,710,507,922,796,892 buckets of tea.<br />
<br />
- Gmaas is "TIRED OF PEOPLE ADDING TO HIS PAGE!!" (Maas 45). EDIT: This is Gmaas's holy, so he wants to have a longer version. For reference, see Maas 3,141,592,653,589,793,238,462. Gmaas is too lazy to write this book himself or to hire someone to do this for him, so he has assembled a group of unpaid freelancers on AoPS to write his holy book for him. He is watching it grow. However, Gmaas sometimes sees a comment that he does not like on the Gmaas article. He possesses an editor of Gmaas and makes him/her delete it. EDIT EDIT: AoPS itself is just an elaborately concealed piece of Gmaas propaganda. EDIT EDIT EDIT: How dare you reveal the truth! *Zaps previous editor out of existence* Now, where were we...<br />
<br />
- Gmaas is a Gmaas who is actually Gmaas. EDIT: Gmaas is omnipotent and omniscient. However, he is not always benevolent.<br />
<br />
- Gmaas has a penguin servant who runs GMAASINC. The penguin may or may not be dead. He had another penguin, who is mostly alive.<br />
- Gmaas owns a TARDIS, and can sometimes be seen traveling to other times for reasons unknown.<br />
<br />
- Gmaas knows how to hack into top secret AoPS community pages. EDIT: AoPS is just Gmaas's elaborately-concealed blog.<br />
<br />
- Gmaas used to be river clan cat who crossed the event horizon of a black hole and came out the other end. EDIT: He eventually created sseraj and has lived with sseraj ever since.<br />
<br />
- Gmaas is king of the first men, the anduls.<br />
<br />
- Gmaas is a well known professor at Meowston Academy. EDIT: He is professor of Gmaasology there. EDIT EDIT: Gmaas founded Meowston Academy. EDIT EDIT EDIT: It is actually called Gmaaston Academy<br />
<br />
- Gmaas comes from Gmaas Land, a magical place where pie is infinite and everything starts with a g<br />
<br />
- Gmaas is the CEO of Caterpillar.<br />
<br />
- Gmaas drinks at Starbucks everyday.<br />
<br />
- Gmaas is addicted to tuna, along with other more potent fish, such as salmon and trout.<br />
<br />
- Gmaas likes turning into fish and catching himself. EDIT: So far, Gmaas has spent 2,718,281 of his many lives as a catfish. However, sometimes, he has been catched as a catfish by other people. Luckily, Gmaas has always escaped.<br />
<br />
- Gmaas won the reward of being cutest and fattest cat ever--he surpassed grumpy cat. (He also out-grumped grumpy cat!!!) EDIT: He is in the Guinness Book of World Records for fluffiest cat ever.<br />
<br />
- He was last sighted at 1665 Alligator Swamp-A 4/1/18 at 3:14:15.92653589793238462 PM.<br />
<br />
- Gmaas is the owner of sseraj, not his pet. EDIT: Gmaas also created sseraj.<br />
<br />
- Gmaas is the embodiment of life, the universe, and beyond.<br />
<br />
- Gmaas watches memes about Gmaas. EDIT: All memes originate with Gmaas, but they are often posted by others.<br />
<br />
- After death Gmaas became the god of hyperdeath and obtained over 9000 souls.<br />
<br />
- One of Gmaas's many real names is Pablo Diego José Francisco de Paula Juan Nepomuceno María de los Remedios Cipriano de la Santísima Trinidad Ruiz y Picasso.<br />
<br />
- Gmaas is a certified Slytherin.<br />
<br />
- Gmaas once slept on sseraj's private water bed, so sseraj locked him in the bathroom. EDIT: Gmaas has superpowers that allowed him to overcome the horrors of Mr. Toilet while locked in the bathroom.<br />
<br />
- Gmaas once sat on an orange on a pile of AoPS books, causing an orange flavored equation explosion.<br />
<br />
- Gmaas conquered the moon and imprinted his face on it until asteroids came and erased it.<br />
<br />
- Gmaas is a supreme overlord who must be given <cmath>1000^{1,000,000,000,000,000,000,000^{1,000,000,000,000,000,000,000}}</cmath> minecraft diamonds. EDIT: Gmaas owns Mojang, but Gmaas sued them when it was supposed to be called Gmaascraft.<br />
<br />
- Gmaas is the Doctor Who lord, sports Dalek-painted cars, and eats human finger cheese, custard, and black holes. EDIT: Gmaas once ate a white hole. Gmaas then exploded and made a new universe.<br />
<br />
- Gmaas is everyone's favorite animal.<br />
<br />
- Gmaas is a Persian Smoke.<br />
<br />
- Gmaas lives with sseraj.<br />
<br />
- Gmaas dislikes geometry but enjoys number theory. EDIT: sseraj once posted a picture of Gmaas being grumpy after seeing an olympiad geometry problem.<br />
<br />
- Gmaas is often overfed (with probability <math>\frac{3972}{7891}</math>), or malnourished (with probability <math>\frac{3919}{7891}</math>) by sseraj. EDIT: Gmaas does not need food. He just eats food because it tastes good.<br />
<br />
- Gmaas has <cmath>\sum_{k=1}^{267795} [k(k+1)]+GMAAS+GMAAAAAAAAAAS</cmath> supercars, excluding the Purrari and the 138838383 Teslas.<br />
<br />
- Gmaas employs AoPS. EDIT: Gmaas is the reason why AoPS exists. EDIT EDIT: Gmaas is the reason why everything exists.<br />
<br />
- Gmaas is a Gmaas with yellow fur and white hypnotizing eyes. EDIT: His fur is not always yellow. His fur can be whatever color he chooses it to be.<br />
<br />
- Gmaas has the ability to divide by zero. EDIT: Gmaas knows what 1/0 is. What is it? We'll never know. EDIT EDIT: 1/0 = 0. How? The power of Gmaas.<br />
<br />
- Gmaas was born with a tail that is a completely different color from the rest of his fur. EDIT: Gmaas can change the color of his fur.<br />
<br />
- Gmaas's stare is very hypnotizing and effective at getting table scraps. EDIT: Gmaas's stare turned Medusa into rock, King Midas into gold, and sseraj into sseraj.<br />
<br />
- Gmaas always appears several minutes before certain classes start as an administrator. EDIT: This is becoming more and more infrequent. Sadly, sseraj rarely posts pictures of Gmaas before classes anymore. EDIT EDIT: Why is this happening? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas is an AoPS administrator under the alias Grayson Maas. EDIT: Gmaas always posts class surveys. He has a fake photo on his bio and has a real one on his community page. However, Gmaas himself has not yet posted on the Gmaas forum. EDIT EDIT: He also has not edited the Gmaas article, the Talk: Gmaas article, the Gmaasology article, or the sseraj article. EDIT EDIT EDIT: The final one is surprising because Gmaas knows more about sseraj than even sseraj does.<br />
<br />
- Gmaas died from too many Rubik's cubes in an Introduction to Algebra A class, but he was revived by the Dark Lord at 12:13:37 AM the next day. EDIT: This was thanks in return for Gmaas reincarnating him during the Triumverate Tournament.<br />
<br />
- It is uncertain whether or not Gmaas is a cat or is merely some sort of beast that has chosen to take the form of a cat (specifically a Persian Smoke). EDIT: He is both. EDIT EDIT: Actually, Gmaas is a cat. Gmaas said so, and science says so. EDIT EDIT EDIT: The profile for Gmaas on the list of AoPS teachers does not mention him being a cat. EDIT EDIT EDIT EDIT: The above post is irrelevant. Gmaas hides his identity under the alias Grayson Maas. EDIT EDIT EDIT EDIT EDIT: Gmaas us everything yet nothing. EDIT EDIT EDIT EDIT EDIT EDIT: How is that? The power of Gmaas.<br />
<br />
- Gmaas is distant relative of the chair of the department of Gmaasology at Princeton. EDIT: In the last few years, many universities have been opening Gmaasology departments. For more information, see the Gmaasology page.<br />
<br />
- Gmaas cannot be Force choked. Darth Vader learned that the hard way...<br />
<br />
- Gmaas is famous, and mods always talk about him before class starts.<br />
<br />
- Gmaas's favorite food is AoPS textbooks because they help him digest problems. EDIT: Gmaas wrote all AoPS textbooks but is never listed in the acknowledgments section.<br />
<br />
- Gmaas tends to reside in sseraj's fridge. EDIT: Gmaas once ate all sseraj's fridge food, so sseraj had to put him in the freezer. EDIT EDIT: Gmaas's fur can protect him from the harsh conditions of a freezer. EDIT EDIT EDIT: Then Gmaas ate all the food in sseraj's freezer. He enjoyed the ice cream in the freezer the most. EDIT EDIT EDIT EDIT: Gmaas also ate sseraj's freezer.<br />
<br />
- Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Gmaas no longer has an Epic Games account. EDIT EDIT: Gmaas created Epic Games, though.<br />
<br />
- Gmaas sightings are not very common. There have only been 30 confirmed sightings of Gmaas in the wild.<br />
<br />
- Gmaas is a sage omniscient cat.<br />
<br />
- Gmaas is looking for suitable places other than sseraj's fridge to live in.<br />
<br />
List of places where Gmaas sightings have happened:<br />
<br />
- The Royal Scoop ice cream store in Bonita Beach Florida<br />
<br />
- Inside the abandoned hospital on Rosevelt Island in New York City, which is also a feral cat sanctuary.<br />
<br />
- MouseFeastForCats/CAT 8 Mouse Apartment 1083<br />
<br />
- Gmaasology 2 (1440)<br />
<br />
- Alligator Swamp A 1072<br />
<br />
- Alligator Swamp B 1073<br />
<br />
- Gmaasology A (1488)<br />
<br />
- Introduction to Gmaasology A (1170)<br />
<br />
- Introduction to Gmaasology B (1529)<br />
<br />
- Welcome to Panda Town Gate 1076<br />
<br />
- Welcome to Gmaas Town Gate 1221<br />
<br />
- Welcome to Gmaas Town Gate 1125<br />
<br />
- 33°01'17.4"N 117°05'40.1"W (Rancho Bernardo Road, San Diego, CA)<br />
<br />
- The other side of the ice in Antarctica<br />
<br />
- Feisty Alligator Swamp 1115<br />
<br />
- Introduction to Gmaasology 1221 (Taught by sseraj)<br />
<br />
- Introduction to Gmaas and Gmaasology 1142<br />
<br />
- Feisty-ish Alligator Swamp 1115 (AGAIN)<br />
<br />
- Advanced Gmaasology and Gmaas Conjuring 1137<br />
<br />
- Intermediate Gmaas and Gmaasology 1207<br />
<br />
- Posting student surveys<br />
<br />
- USF Castle Walls - Elven Tribe 1203<br />
<br />
- The Dark Lord's Hut 1210<br />
<br />
- Gmathamatical Problem Series 1200<br />
<br />
- Intermediate Gmaasology 1138<br />
<br />
- Intermediate Number Theory 1476<br />
<br />
- Introduction to Gmaasology 1204 on July 27, 2016<br />
<br />
- Gmaasology B 1112<br />
<br />
- Intermediate Algebra 1561 7:17 PM 12/11/16<br />
<br />
- Nowhere Else, Tasmania<br />
<br />
- The Gmaathamatics School of Gmaasology<br />
<br />
- Geometry 1694 at 1616 PST military time. There was a boy riding him, and he seemed extremely miffed.<br />
<br />
- Intermediate Gmaasology 1710 9/24/2018<br />
<br />
- Introduction to Gmaasology 1369<br />
<br />
- Introduction to Gmaas and Gmaasology 1177<br />
<br />
Here are some more deleted sighting from an old version of Gmaas:<br />
<br />
- Cat Gathering 1222<br />
<br />
− Introduction to Geometry 1190<br />
<br />
− Cat Meow Meow Purr 1110<br />
<br />
− Introduction to Gmaasology 1447<br />
<br />
− Introduction to Geometry 1535<br />
<br />
− Introduction to Gmaasology A 1392<br />
- Everywhere<br />
<br />
- These have all been designated as the most glorious sections of AoPSland now (especially the USF castle walls), but deforestation is so far from threatens the wild areas (i.e. Alligator Swamps A&B).<br />
<br />
- Gmaas has also been sighted in Olympiad Gmaasology 1148.<br />
<br />
- Gmaas has randomly been known to have sent his minions into Gmaasology 2 1163. However, the danger is passed. That class is over.<br />
<br />
- Gmaas once snuck into sseraj's email so he could give a future Gmaasologist an extension in Introduction to Gmaasology 1204. This was 1204 minutes after his sighting on 7/27/16.<br />
<br />
- Gmaas has randomly appeared on top of the USF's Tribal Bases(he seems to prefer the Void Tribe). However, the next day there is normally a puddle in the shape of a cat's underbelly wherever he was sighted. Nobody knows what this does. EDIT: Nobody has yet seen him atop a tribal base yet.<br />
<br />
- Gmaas is often under the disguise of a penguin or cat. Look out for them. EDIT: Gmaas rarely disguises himself as a penguin. EDIT EDIT: He is a cat. EDIT EDIT EDIT: He can be whatever he wants. EDIT EDIT EDIT EDIT: But he likes penguins. (As snacks.)<br />
<br />
- Gmaas lives in the shadows. Is he a dream? Truth? Fiction? Condemnation? Salvation? AoPS site admin? He is all these things and none of them. He is... Gmaas. EDIT: He is an AoPS site admin. EDIT EDIT: He exists. EDIT EDIT EDIT: He is everything.<br />
<br />
- If you make yourself more than just a cat... if you devote yourself to an ideal... and if they can't stop you... then you become something else entirely. A LEGEND. Gmaas now belongs to the ages. EDIT: Gmaas belongs to Gmaas.<br />
<br />
- Is this real life? Is this just fantasy? No, this is Gmaas, the legend. EDIT: This is real life.<br />
<br />
- Aha!! An impostor!!<br />
<br />
http://www.salford.ac.uk/environment-life-sciences/research/applied-archaeology/greater-manchester-archaeological-advisory-service<br />
<br />
(Look at the acronym.)<br />
<br />
GREATER MANCHESTER ARCHAEOLOGICAL ADVISORY SERVICE EDIT: The above fact is slightly irrelevant. EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant.<br />
<br />
- Gmaas might have been viewing (with a <math>\frac{99999.\overline{9}}{100000}</math> chance) the Ultimate Survival Forum. He (or is he a she?) is suspected to be transforming the characters into real life. Be prepared to meet your epic swordsman self someday. If you do a sci-fi version of USF, then prepare to meet your Overpowered soldier with amazing weapons one day.EDIT: Gmaas is neither he nor she, Gmaas is above gender. EDIT EDIT: Gmaas is above your door, waiting to pounce on you.<br />
<br />
- Gmaas is love; Gmaas is life. EDIT: Gmaas is a cat. EDIT EDIT: Gmaas can be whatever he wants to be because he is omnipotent. How? The power of Gmaas.<br />
<br />
- The name of Gmaas is so powerful that it radiates Deja Mew.<br />
<br />
- Gmaas is on the list of "Elusive Creatures." If you have questions or want the full list, contact Gmaas himself. That is if you can figure out how to contact him. He doesn't have an email address nor an address to send mail to. In fact nobody knows for sure where he lives or what he looks like. They can only guess and imagine.<br />
<br />
- Gmaas can be summoned using the <math>\tan(90)</math> ritual. Draw a pentagram and write the numerical value of <math>\tan(90)</math> in the middle, and he will be summoned. EDIT: The above fact is incorrect. A user has done this and commented with screenshot proof at the below link, but Gmaas was not summoned. https://artofproblemsolving.com/community/c287916h1291232 EDIT EDIT: The above 'proof' is non-conclusive. The user had only put an approximation.<br />
<br />
- Gmaas's left eye contains the singularity of a black hole if and only if everyone in the world blinks at the same time within a nanosecond. EDIT: That has never happened and thus it does not contain the singularity of a black hole.<br />
<br />
- Lord Grindelwald once tried to make Gmaas into a Horcrux, but Gmaas's fur is protected by the Elder Wand and secure.<br />
<br />
- Despite common belief, Harry Potter did not defeat Lord Voldemort. Gmaas did. EDIT: Harry Potter was actually Gmaas in disguise.<br />
<br />
- The original owner of Gmaas was Gmaas. EDIT: Gmaas will always be the sole owner of Gmaas. [[sseraj]] is just Gmaas's pet.<br />
<br />
- Gmaas was not the fourth Peverell brother, but he ascended into a higher being and now he resides in the body of a cat, as he was before. Is it a cat? We will know. (And the answer is YES.) EDIT: He wasn't the fourth Peverell brother, but he was a cousin of theirs, and he advised Ignotus to give up his cloak.<br />
<br />
- Gmaas may be ordering his cyber hairballs to take the forums, along with microbots. EDIT: His fur is so long that it generates thousands of micro-hairballs per day. EDIT EDIT: However, Gmaas no longer sheds. Most of Gmaas's hairballs are made when Gmaas gets a haircut. EDIT EDIT EDIT: Gmaas hates haircuts.<br />
<br />
- Gmaas rarely frequents the headquarters of the Illuminati. He was their symbol for one yoctosecond, but he soon decided that the job was too low for his power to be wasted on.<br />
<br />
- It has been wondered if Gmaas is the spirit of Obi-Wan Kenobi or Anakin Skywalker in a higher form, due to his strange capabilities and powers. EDIT: Gmaas is neither Anakin Skywalker or Obi-Wan Kenobi as he is trillions of years older. EDIT EDIT: Anakin Skywalker and Obi-Wan Kenobi could have been Gmaas in another form or reincarnated.<br />
<br />
- Gmaas has a habit of sneaking into computers, joining The Network, and exiting out of some other computer. EDIT: Gmaas invented the first computer. He gave it to Charles Babbage for his birthday.<br />
<br />
- Gmaas uses gmewal as his email service. Edit: gnewal went out of business, so Gmaas now doesn't have an email address<br />
<br />
- Gmaas has a bright orange tail with hot pink spirals. Or he had for 15 minutes. That was the 15 minutes after he tried to play Taylor Swift music on his 34,000 year old MP3 player in front of sseraj, who, at the time, was handling a bucket of dangerous, radioactive material.<br />
<br />
- Gmaas is well known behind his stage name, Michael Stevens (also known as Vsauce XD), or his page name, Purrshanks. EDIT: Crookshanks was his brother.<br />
<br />
- Gmaas watchers know that the codes above are NOT years. They are secret codes for the place. But if you've edited that section of the page, you know that. EDIT: The above post is false. The post before the above post has an unknown truth value.<br />
<br />
- Gmaas is a good friend of the TARDIS and the Millennium Falcon.<br />
<br />
- In the Dark Lord's hut, Gmaas was seen watching Doctor Who. Anyone who has seen the Dark Lord's hut knows that both Gmaas and the DL (USF code name of the Dark Lord) love BBC. How Gmaas gave him a TV may be lost to history. And it has been lost.<br />
<br />
- The TV has been noticed to be invincible. Many USF weapons, even volcano rings, have tried (and failed) to destroy it. The last time it was seen was on a Kobold display case outside of a mine. The display case was crushed, and a report showed a spy running off with a non-crushed TV.<br />
<br />
- The reason why Dacammel left the USF is that gmaas entrusted his TV to him, and not wanting to be discovered by LF, Cobra, or Z9, dacammel chose to leave the USF, but is regretting it, as snakes keep spawning from the TV. EDIT: The above fact is somewhat irrelevant. EDIT EDIT. Dacammel gave the TV back to gmaas, and he left the dark side and their cookies alone. EDIT EDIT EDIT: The above fact is relevant. EDIT EDIT EDIT EDIT: Is this the longest chain of edits on AoPS Wiki? EDIT EDIT EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT EDIT EDIT: It is.<br />
<br />
- Gmaas is a Super Duper Uper Cat Time Lord. He has ERROR: NUMBER COULD NOT COMPILE: TOO LONG regenerations and has used<math>3</math>. <cmath>9\cdot12\cdot2\cdot267794=57843504</cmath>.<br />
<br />
- Gmaas highly enjoys destroying squeaky toys until he finds the squeaky part, then destroys the squeaky part. EDIT: In that way Gmaas is similar to a dog.<br />
<br />
- Gmaas loves to eat turnips. At<math> (Error compiling LaTeX. ! Missing </math> inserted.)\frac{13}{32}<math>of the sites he was spotted at, he was seen with a turnip.<br />
<br />
- Gmaas has a secret hidden garden full of turnips under [[sseraj]]'s house.<br />
<br />
- [[sseraj]] is "Gmaas's person."<br />
<br />
- Gmaas has three tails, one for everyday life, one for special occasions, and one that is invisible.<br />
<br />
- Gmaas is a dangerous creature. If you ever meet him, immediately join his army or you will be killed. EDIT: If you ever meet Gmaas, scratch him on the ears. Most cats enjoy that.<br />
<br />
- Gmaas is in alliance with the Cult of Skaro. How did he get an alliance with ruthless creatures that want to kill everything in sight? Nobody knows (except him), not even the leader of the Cult of Skaro.<br />
<br />
- Gmaas lives in Gallifrey and in Gotham City. (He has sleepovers with Batman.)<br />
<br />
- Gmaas is an excellent driver. EDIT: He designed the first driver's license test, although he didn't bother with the permit test. EDIT EDIT: He invented the first car in 1600, but it sunk in the Pacific Ocean. No one has seen it ever since.<br />
<br />
- The native location of Gmaas is the twilight zone.<br />
<br />
- Donald Trump once sang "All Hail the Chief" to Gmaas, 3 days after being sworn in as US President.<br />
<br />
- Gmass likes to talk with Ricard Rusczyk from time to time.<br />
<br />
- Dumbledore never died. Dumbledore was Gmass. Gmass was Death. Gmass is gave the 3 deathly hallows to the 3 brothers. EDIT: Of course Gmass is the entire reason Voldemort is gone now. EDIT EDIT: like we said before, Gmass was Harry Potter. EDIT EDIT: If Gmass hadn't done this, h we all would have been dead cause of Voldemort. EDIT EDIT EDIT: SOOOOO U BETTER BE THANKFULL!!!!!!<br />
<br />
- Gmaas is the reason why the USF has the longest thread on AoPS.<br />
<br />
- [[sseraj]], in 1521 Introduction to Number Theory, posted an image of Gmaas after saying "Who wants to see 5space?" at around 5:16 PM Mountain Time, noting Gmaas was "also 5space". EDIT: He also did it in Introduction to Algebra A once.<br />
<br />
- Gmaas is not retarded. EDIT: Gmaas is the smartest living being on the planet.<br />
<br />
- In Introduction to Number Theory 1521, [[sseraj]] posted an image of a 5space Gmaas fusion. (First sighting) EDIT: It was also confirmed that Gmaas doesn't like ketchup because it was the only food left the photo.<br />
<br />
- In 1447 Introduction to Geometry, [[sseraj]] posted a picture of Gmaas with a Rubik's cube suggesting that Gmaas's has an average solve time of</math> (Error compiling LaTeX. ! Missing <math> inserted.)-GMAAS</math>seconds.<br />
<br />
- Gmaas beat Superman in a fight with ease. EDIT: Gmaas infiltrated Superman's body, then made him kill himself. So, Superman killed Superman.<br />
<br />
- Gmaas is an admin of Roblox. EDIT: He created Roblox.<br />
<br />
- Gmaas traveled around the world, paying so much <math>MONEY</math> just to eat.<br />
<br />
- Gmaas is a confirmed Apex predator and should not be approached, unless in a domestic form.<br />
<br />
Summary of Gmaas's many powers and deeds:<br />
<br />
- When Gmaas subtracts <math>0.\overline{99}</math> from <math>1</math>, the difference is greater than <math>0</math>.<br />
<br />
- Gmaas was shown to have fallen on Wed Aug 23 2017: https://ibb.co/bNrtmk https://ibb.co/jzUDmk<br />
<br />
- Gmaas died on August 24, 2017, but his father, Gmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasrevived him after about 2 mins of being dead.<br />
<br />
- The results of the revival are top secret, and nobody knows what happened.<br />
<br />
- [[sseraj]], in 1496 [[Gmaasology]] 2, said that Gmaas is Santacat.<br />
<br />
- [[sseraj]] likes to post a picture of Gmaas in every class he passes by. EDIT: [[sseraj]] always posts pictures of Gmaas in cat form, but never in polar bear form. EDIT EDIT: Gmaas is rarely in polar bear form.<br />
<br />
- [[sseraj]] posted a picture of Gmaas as an Ewok, suggesting he resides on the moon of Endor. Unfortunately, the moon of Endor is also uninhabitable ever since the wreckage of the Death Star changed the climate there. It is thought Gmaas is now wandering space in search for a home. EDIT: What evidence is there Endor was affected? Other Ewoks still live there. EDIT EDIT: Also, Gmaas doesn't care. He can live there no matter what the climate is. EDIE EDIT EDIT: Gmaas is omnipotent and can live anywhere he wants during his many lives.<br />
<br />
- Gmaas is the lord of the pokemons.<br />
<br />
- Gmaas can communicate with, and sometimes control, any other cats; however, this is very rare, as cats normally have a very strong will.<br />
<br />
- A picture of Gmaas: http://i.imgur.com/PP9xi.png<br />
<br />
- Gmaas met Mike Miller. EDIT: Gmaas ate Mike Miller.<br />
<br />
- Gmaas got mad at [[sseraj]] once, so Gmaas locked [[sseraj]] in [[sseraj]]'s freezer.<br />
<br />
- Then, [[sseraj]] decided to eat all of Gmaas's hidden turnips in the freezer as punishment. EDIT: [[sseraj]] could not eat all of them so, he put the remaining turnips in the fire.<br />
<br />
- Gmaas once ate a pie.<br />
<br />
- A Gmaas bite is 314159265358979323846264 psi.<br />
<br />
- Many people have met Gmaas, although many of these sightings are dubious. EDIT: It is just like alien sightings.<br />
<br />
- Gmaas can talk but normally hates talking.<br />
<br />
- Gmaas likes to eat his own fur. That's why he doesn't have any as of late<br />
<br />
- Gmaas is bigger than an ant. EDIT: so is a regular cat <br />
<br />
- Gmaas once ate the king of the ants. EDIT: Ants do not have kings; they have queens.<br />
<br />
- Gmaas lives somewhere over the rainbow. EDIT: He lives in [[sseraj]]'s house. EDIT EDIT: [[sseraj]] lives somewhere over the rainbow.<br />
<br />
- Gmaas is an obviously omnipotent cat.<br />
<br />
- [[sseraj]] is known to post pictures of Gmaas on various AoPS classrooms. It is not known if these photos have been altered with the editing program called 'Photoshop.'<br />
<br />
- Gmaas<br />
<br />
- [[sseraj]] has posted pictures of Gmaas in Introduction to Algebra before class started with the title "caption contest." Anyone who posted a caption mysteriously vanished in the middle of the night. EDIT: This has happened many times, including in Introduction to Geometric [[Gmaasology]] 1533, among other active classes. The person writing this did participate, and did not disappear. (You could argue Gmaas is typing this through his/her account...)<br />
<br />
- Gmaas once slept in your bed and made it gray.<br />
<br />
- Richard Rusczyk actually Gmaas in disguise. EDIT: That is false. Gmaas is only in one form at a time. EDIT EDIT: This is also false, you are Gmaas and Gmaas owns you.<br />
<br />
- Gmaas is suspected to be a cat in disguise. EDIT: He is a cat in disguise. See the results on the Gmaas poll in the Gmaas forum.<br />
<br />
- Gmaas is a cat but has characteristics of every other animal on Earth. EDIT: Gmaas does not have the characteristic of being able to eat plankton. EDIT EDIT: Yes he does. He just has not decided to reincarnate as a blue whale yet.<br />
<br />
- Pegasus was modeled off Gmaas. EDIT: Pegasus used to be Gmaas's pet, but Pegasus escaped and joined Bellerophon.<br />
<br />
- Gmaas is the ruler of the universe and has been known to be the creator of the species "Gmaasians". EDIT: He is the universe<br />
<br />
- There is a rumor that Gmaas is starting a poll. EDIT: He has. It is on the Gmaas forum, made by his minions.<br />
<br />
- Gmaas is a Persian smoke who ran away, founded GmaasClan, and became a kitty-pet.<br />
<br />
- There is a sport called "Gmaas Hunting" where people try to successfully capture Gmaas in the wild with video/camera/eyes. Strangely, no one has been able to do this, and those that have have mysteriously disappeared into the night. Nobody knows why. Many people have tried Gmaas Hunting, but they never have been successful.<br />
<br />
- Gmaas burped and caused an earthquake.<br />
<br />
- Gmaas once drank from a teacup.<br />
<br />
- GMAAS IS HERE.... PURRRRRRRRRRRRRRRRRRRR EDIT: Gmaas is everywhere. EDIT EDIT: He is behind you.<br />
<br />
- Gmaas made and currently owns the Matrix. EDIT: The above fact is true. Therefore, this is an illusion.<br />
<br />
- Gmaas is the reason Salah will become better than Ronaldo.<br />
<br />
- Who is Gmaas, really? EDIT: Gmaas is a cat.<br />
<br />
− Gmaas is a heavenly being. EDIT: He is immortal.<br />
<br />
- Gmaas is a cat with no fur or tail. In fact he's a human wearing a cat costume. <br />
- Illuminati was a manifestation of Gmaas, but Gmaas decided Illuminati was not great enough for his godly self.<br />
<br />
- [[sseraj]] has met Gmaas, and Gmaas is his best friend. EDIT: [[sseraj]] is Gmaas's great great great great great grandson.<br />
<br />
- Gmaas read Twilight. EDIT: ...and SURVIVED.<br />
<br />
- There is a secret code when put into super smash where Gmaas would be a playable character. Too bad he didn't say it.<br />
<br />
- Gmaas was a tribute to one of the Hunger Games, came out a Victor, and now lives in District 4.<br />
<br />
- Gmaas is the only known creature that will survive the destruction of Earth in 99,999,999 years. EDIT: The Earth will probably die in around 5,000,000,000 years.<br />
<br />
- [[5space]] (side admin) is one of Gmaas's slaves. EDIT: Gmaas owns all AoPS site administrators. EDIT EDIT: He owns Himself.<br />
<br />
Gmaas photos − http://cdn.artofproblemsolving.com/images/f/f/8/ff8efef3a0d2eb51254634e54bec215b948a1bba.jpg<br />
<br />
http://disneycreate.wikia.com/wiki/File:Troll_cat_gif_(1).gif<br />
<br />
He was also sighted here.<br />
<br />
Gmaas in Popular Culture:<br />
<br />
- BREAKING NEWS: A Gmaasologist has found a possible cousin to Gmaas in Raymond Feist's book Silverthorn. They are mountain dwellers, gwali. Not much are known about them either, and when someone asked,"What are gwali?" the customary answer "This is gwali" is returned. Another eminent Gmaasologist is now looking into it.<br />
<br />
- Someone is writing a book about Gmaas.<br />
<br />
- Sighting of Gmaas: https://2017.spaceappschallenge.org/challenges/warning-danger-ahead/and-you-can-help-fight-fires/teams/gmaas/project<br />
<br />
- Oryx the mad god is actually Gmaas wearing a suit of armor. This explains why he is never truly killed.<br />
<br />
- Potential sighting of Gmaas [1]<br />
<br />
- Gmaas has been spotted in some Doctor Who and Phineas and Ferb episodes, such as Aliens of London, Phineas and Ferb Save Summer, Dalek, Rollercoaster, Rose, Boom Town, The Day of The Doctor, Candace Gets Busted, and many more.<br />
<br />
- Gmaas can be found in many places in Plants vs. Zombies Garden Warfare 2 and Bloons TD Battles.<br />
<br />
- Gmaas was an un-credited actor in the Doctor Who story Knock Knock, playing a Dryad. How he shrunk, we will never know.<br />
<br />
- An eminent Gmaasologist is also writing a story about him. He is continuing the book that was started by the professor of Gmaasology at Harvard. When he is done he will post it here.<br />
<br />
- Gmaas is a time traveler from 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 B.C.<br />
<br />
- No one knows if Gmaas is a Mr. Mime in a cat skin, the other way around, or just a downright combination of both. EDIT: Gmaas is an immortal in a cat body.<br />
<br />
- In it, it mentions these four links as things Gmaas is having trouble (specifically technical difficulties). What could it mean? Links:<br />
<br />
https://docs.google.com/document/d/1NZ0XcFYm80sA-fAoxnm7ulMCwdNU75Va_6ZjRHfSHV0<br />
<br />
https://docs.google.com/document/d/1ELN7ORauFFv1dwpU_u-ah_dFJHeuJ3szYxoeC1LlDQg/<br />
<br />
https://docs.google.com/document/d/1oy9Q3F7fygHw-OCWNEVE8d-Uob2dxVACFcGUcLmk3fA<br />
<br />
https://docs.google.com/document/d/1jzb9Q6FmDmrRyXwnik3e0sYw5bTPMo7aBwugmUbA13o<br />
<br />
- Another possible Gmaas sighting?<br />
<br />
-<math> (Error compiling LaTeX. ! Missing </math> inserted.)Another<math>sighting? [3]<br />
<br />
- Yet Another Gmaas sighting? [4]<br />
<br />
- Gmaas has been sighted several times on the Global Announcements forum.<br />
<br />
- Gmaas uses the following transportation: <img> http://cdn.artofproblemsolving.com/images/3/6/8/368da4e615ea3476355ee3388b39f30a48b8dd48.jpg </img><br />
<br />
- When Gmaas was angry, he started world wars 1 & 2. It is only because of Gmaas that we have not had World War 3. EDIT: He was starting to have to get angry in the Cold War, especially around the Cuban Missile Crisis and the Ronald Regan era, but he decided to eat food, which calmed him down.<br />
<br />
- Gmaas is the only cat to have been proved irrational and transcendental, though we suspect all cats fall in the first category.<br />
<br />
- Gmaas belongs to a secret club of transcendental cats. EDIT: That club is located underneath the Eiffel Tower. EDIT EDIT: Gustave Eiffel was Gmaas in disguise and designed the club.<br />
<br />
- Gmaas plays Geometry Dash. His username is D3m0nG4m1n9. EDIT: Gmaas only does this to punish himself. Olympiad Geometry is his least favorite thing to do.<br />
<br />
- Gmaas likes to whiz on the wilzo.<br />
<br />
- Gmaas has been spotted in many AoPS classes, such as AMC 8 Basics. EDIT: Many of the AoPS classes Gmaas has visited can be found in the Gmaas sightings section of this article.<br />
<br />
- Gmaas is cool. EDIT: He was not cool in summer, so he invented air conditioning. EDIT EDIT: He is air conditioning, in fact he is the entire universe.<br />
<br />
- Gmaas hemoon card that does over 9000000 dmg.<br />
<br />
- Gmaas is a skilled swordsman who should not to be mistaken for Puss in Boots. Some say he even trained the mysterious and valiant Meta Knight.<br />
<br />
- Kirby once swallowed Gmaas. Gmaas had to spit him out.<br />
<br />
- Gmaas was the creator of pokemon, and his pokemon card can OHKO anyone in one turn. He is invisible and he will always move first.<br />
<br />
- Gmaas beat Dongmin in The Genius Game Seasons 1, 2, 3, 4, 5, 6, and 7.<br />
<br />
- Gmaas has five letters. Pizza also has five letters. Pizzas are round. Eyes are round. There is an eye in the illuminati symbol. EDIT: Gmaas is a fluffy cat.<br />
<br />
- Gmaas knows both 'table' and 'tabular' in LaTeX, and can do them in his sleep. EDIT: Gmaas invented LaTeX in his sleep.<br />
<br />
- Gmaas does not hate cheddar cheese, but he doesn't love it either.<br />
<br />
- Gmaas is a cat and not a cat. EDIT: He is a cat.<br />
<br />
- Gmaas was born on the sun. EDIT: Not the sun, the suns. He was born on all the suns at once.<br />
<br />
- Gmaas eats tape. EDIT: Gmaas invented tape. EDIT EDIT: Gmaas eats everything. Gmaas eats computers.<br />
<br />
- Gmaas likes Bubble Gum.<br />
<br />
- Thomas Edison did not invent the lightbulb; Gmaas did.<br />
<br />
- Gmaas invented the alphabet. EDIT: Gmaas thought that hieroglyphs were too complicated, so he invented the alphabet.<br />
<br />
- Gmaas eats metal. EDIT: Gmaas once ate so much metal that he turned into a bronze statue.<br />
<br />
- Gmaas is over 9000 years old! EDIT: This is just a DBZ reference, and bears no reality to his true age. EDIT EDIT: Gmaas is trillions of years old.<br />
<br />
- Gmaas is a cat and not a cat. EDIT: He is a cat. EDIT EDIT: This fact has been stated 31,415 times in this article.<br />
<br />
- Gmaas started the Iron Age. EDIT: He thought civilization was getting too advanced. So he sent out the Sea People to destroy civilization.<br />
<br />
- Gmaas made the dinosaurs go extinct. EDIT: That happened when he got angry that a dinosaur stepped on his toe.<br />
<br />
- Gmaas created life.<br />
<br />
- Gmaas created AoPS. EDIT: AoPS was actually born out of a small fraction of Gmaas's abstract reality, and only the sheer amount math can keep it here. (It is also rumored that when he reclaims it, the USF will be deleted, as that is where 83% of the factions of his abstract reality lives, and when people leave USF, more and more escapes.)<br />
<br />
− Gmaas created mathematics.<br />
<br />
- Gmaas does not like Roblox.<br />
<br />
- Gmaas told Steve Jobs to start a company.<br />
<br />
- Gmaas invented Geometry Dash. EDIT: Gmaas hates Olympiad Geometry. [Source: [[sseraj]]]<br />
<br />
- Gmaas got to</math> (Error compiling LaTeX. ! Missing <math> inserted.)infty</math>in Flappy Bird.<br />
<br />
- Gmaas invented Helix Jump.<br />
<br />
- Gmaas can play Happy Birthday on the Violin.<br />
<br />
- Gmaas has mastered Paganini. EDIT: Paganini was Gmaas in disguise. EDIT EDIT: Gmaas was Paganini in one of his 100,000 human lives. He does not have a human life now because he has a cat life.<br />
<br />
- Gmaas discovered Atlantis after one dive underwater.<br />
<br />
- Gmaas made a piano with 89 keys. EDIT: The piano was made out of chocolate. EDIT: He also made a piano bench made out of chocolate.<br />
<br />
- Gmaas can see the future and how to change it.<br />
<br />
- Gmaas has every super power you can imagine. EDIT: Gmaas has more superpowers than you can imagine.<br />
<br />
- Gmaas made a Violin with 9 strings.<br />
<br />
- Gmaas can read 5 books at once. EDIT: It is slightly difficult for Gmaas to do this because he has no fingers. But somehow, Gmaas finds a way. EDIT: He uses his mind to hold open the books.<br />
<br />
- Gmaas eats rubber bands. EDIT: Gmaas once reincarnated as a rubber band. He thought it was the worst period in his life. Eventually he was snapped and reincarnated as a bacterium, which was also boring.<br />
<br />
- Gmaas married Mrs. Norris. EDIT: Mrs. Norris is his second worst enemy. They say keep your enemies close. EDIT: Gmaas eventually divorced Mrs. Norris for her astounding lack of inteligence and short life span.<br />
<br />
- Gmaas can fly faster than anything. EDIT: No one can travel faster than light. EDIT EDIT: Gmaas can.<br />
<br />
- Grumpy cat is his son. EDIT: Grumpy cat is his worst enemy and his son.<br />
<br />
- Gmaas eats paper. EDIT: According to Gmaas, recycled paper tastes the very good. Paper with steak juice on it tastes even better.<br />
<br />
- Gmaas likes lollipops. EDIT: Gmaas was reincarnated as a lollypop. He did not appreciate having spit all over him while he dissolved.<br />
<br />
- Gmaas nibbles on pencils.<br />
<br />
- Gmaas is alive. EDIT: He is both alive and dead. (For reference, see later post.) EDIT EDIT: He can make people alive and dead.<br />
<br />
- Gmaas is Ninja in Fortnite. EDIT: Gmaas possesses Ninja in Fortnite.<br />
<br />
- Gmaas is love; Gmaas is life. EDIT: Scientist do not know how life was formed. Gmaas does.<br />
<br />
- Gmaas taught Richard Rusczyk everything he knows about mathematics. EDIT: Many famous mathematicians have been Gmaas in disguise.<br />
<br />
- Gmaas can control matter by looking at it. EDIT: He once looked at a galaxy while he was angry. Everything in the galaxy exploded.<br />
<br />
- Gmaas created AoPS. EDIT: He created 99% of all websites. 98% of those websites are blank and unreachable, but the ones that are not are interesting.<br />
<br />
- Gmaas is a quantum particle. EDIT: Gmaas is multiple quantum particles. He is a macroscopic collection of them.<br />
<br />
- Gmaas is alive and dead at the same time. EDIT: He is usually alive.<br />
<br />
- Gmaas likes snow. EDIT: Once Gmaas was reincarnated as a polar bear around 1,000,000 years ago. He had the best time of his lives. EDIT EDIT: While he was a polar bear, he ate many fish.<br />
<br />
- GMAAS LIKES THE NEW AOPS UPDATE! EDIT: Are you sure he does? Did you ask him? EDIT EDIT: Yes, I did.<math> (Error compiling LaTeX. ! Missing </math> inserted.)\text{Gmaas is right behind you}<math>EDIT: Gmaas is everywhere. He is in a quantum superposition. He is still in the superposition until someone sees him. The chance of him being behind you is 0.0000000000000000000000000000000000000000000000000000001%. But, you never know. Is he behind you? Is he behind me right now? He is!!! Aaaaaaaaaah... THUMP<br />
<br />
- Gmaas likes his eggs hard boiled.<br />
<br />
- Gmaas doesn't take showers; he only takes bloodbaths.<br />
<br />
- When the bogeyman goes to sleep, he checks his closet for Gmaas.<br />
<br />
- When Gmaas crosses the street, cars have to look both ways.<br />
<br />
- Gmaas has counted to infinity an infinite amount of times.<br />
<br />
- Gmaas pulled the pin in a grenade. 1 billion people died. Then he threw it.<br />
<br />
- Gmaas controls the Illuminati and controls all the world's resources. He also is the ruler of a communist society on Mars.<br />
<br />
- Gmaas has taken the AHSME/AMC 10, AIME, USAJMO, USAMO, and IMO all the years it has come out. It is rumored that for 2018, Gmaas got a 163.5 on the AMC 12A, a 156 on the AMC 12B, and 17 problems right on the AIME I. EDIT: He also got 51 on USAMO.<br />
<br />
- Gmaas has designed most of the AMC tests. EDIT: He didn't design them in 2015 because he was hibernating too long.<br />
<br />
- Gmaas is a koala. EDIT: Gmaas was actually the first koala. He wanted to reincarnate himself into something new, so he created a whole other species. [Source Wikipedia: Koala] EDIT: Gmaas is a Koala when they are not alive, which is 10% of the time. When they are alive, Gmaas is a cat.<br />
<br />
- Time is Gmaas's vacation home. EDIT: Gmaas created time as a science project.<br />
<br />
- Gmaas was once reincarnated as Chuck Norris, but he missed being a cat. Then he became a cat.<br />
<br />
- Gmaas once resided with a certain physicist named Schrödinger, but he left because Schrödinger was too confusing. Granted, nothing is too confusing for Gmaas but Schrödinger also made Gmaas alive and dead, which felt weird.<br />
<br />
- Gmaas once decided to eat a carrot. He decided turnips were better.<br />
<br />
- [[Gmaasology]] used to be called [[Gmaathamatics]]. It was renamed a few years ago. For more information, see the [[Gmaasology]] page. That page needs expanding.<br />
<br />
- \gmaas should be made into a LaTeX command. Its function should be to summon Gmaas.<br />
<br />
-</math> (Error compiling LaTeX. ! Missing <math> inserted.)\gmaas</math><br />
<br />
- Grumpy cat pretends to be a descendent of Gmaas because he is jealous. He is not a descendant of Gmaas.<br />
<br />
- Every IMO Gold Medalist is two of Gmaas, standing on top of each other in a trenchcoat.<br />
<br />
- Gmaas has been everywhere in the world. EDIT: Gmaas has been everywhere in the universe and multiverse.<br />
<br />
- The degree used to be called the Gmaas Arc, but the name was too long for most people, so they switched the name.<br />
<br />
- Gmaas is famous on AoPS. EDIT: Gmaas is AoPS.<br />
<br />
- Gmaas invented every math theorem and in fact invented math.<br />
<br />
- Gmaas made 31.415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983% of memes. EDIT: This is incorrect. This is only an estimate.<br />
<br />
- Gmaas is a Gmaas since Gmaas likes to Gmaas and Gmaas is cool because he is named Gmaas.<br />
<br />
- Gmaas once ate Big Chungus. EDIT: Gmaas also once ate cat food. EDIT EDIT: Gmaas hates cat food. EDIT EDIT EDIT: Gmaas also hates dog food. EDIT EDIT EDIT EDIT: Gmaas does not need to eat, he is an all-conquering god who never/rarely dies. EDIT EDIT EDIT EDIT EDIT: Gmaas is Big Chungus EDIT EDIT EDIT EDIT EDIT EDIT: He was Big Chungus for 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745530506820349625245174939965143142980919065925093722169646151570985838741059788595977297549893016175392846813826868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388439045124413654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767889525213852254995466672782398645659611635488623057745649803559363456817432411251507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858900971490967598526136554978189312978482168299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610213596953623144295248493718711014576540359027993440374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927819119793995206141966342875444064374512371819217999839101591956181467514269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672218256259966150142150306803844773454920260541466592520149744285073251866600213243408819071048633173464965145390579626856100550810665879699816357473638405257145910289706414011097120628043903975951567715770042033786993600723055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816909152801735067127485832228718352093539657251210835791513698820914442100675103346711031412671113699086585163983150197016515116851714376576183515565088490998985998238734552833163550764791853589322618548963213293308985706420467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325974636673058360414281388303203824903758985243744170291327656180937734 seconds. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: This is only an rough estimate<br />
<br />
- Garfield is Gmaas in disguise. EDIT: But Gmaas also created Garfield. He took a Gar and a Field, and added them. Boom. He made Garfield.<br />
<br />
-Gmaas didn't create the world. He didn't create the universe. The didn't create multiverses. He is the world. He is the universe. He is the multiverses<br />
<br />
-Gmaas has a cult with many followers. This is the page for his followers. They pray to him and remember him for his deeds.<br />
<br />
- Garfield ate Gmaas but then Gmaas ate garfield. Then they ate each other. <br />
<br />
- Gmaas has an existential crisis every 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374 seconds.<br />
<br />
- Gmaas married and then divorced a picture of himself EDIT: He then destroyed all evidence of this by swallowing it and barfing it out as a hairball<br />
<br />
- Gmaas needed light to read and he turned into a lamp called the sun and created 31.41592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346760842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769752456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983% of life. EDIT: Gmaas uses a new type of tetradecimal number system where the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, G, M, A, and S. The number 416877 is Gmaas's favorite integer. (Convert it to this number system)<br />
<br />
-None of this is true. Except for maybe that last one. EDIT: This fact is therefore not true.<br />
<br />
-Gmaas has controlled everyone's mind and made them eat moldy cheeseburgers.<br />
<br />
-You can't PM or email Gmaas. He's a pretty tough guy to talk to. He makes the great hulk look like a mouse. To contact him you have to summon Gmaas' royal guards at his palace. Or you can contact him using a sophisticated and secretive instant messaging system. Which is really just pretending to read minds. <br />
<br />
- remember, EVERY SINGLE thing u do, Gmaas is watching, and when u do bad, or insult him, u will feel regret very soon.Also, if u find cat hair everywhere, but u r not a cat owner,<br />
he is probably visiting your home to see how much math u we doing. So START DOING YOUR MATH KIDS! <br />
<br />
-<aops>X</aops]>sseraj locked Gmaas in his toilet because Gmaas blew the top half of his house.<br />
<br />
-Gmaas once woke up one day, farted, and accidentally created the known universe.<br />
<br />
-Gmaas can destroy every living creature and every imaginary creature, including himself, using only 1% of his power. EDIT: That means he can destroy himself, but he defeats everyone, so this is a paradox. However, this is still possible because of the power of GMAAS.<br />
<br />
-Spelling Gmaas with a lowercase G is disrespectful. Such a insult shall never happen, or the world may be imbalanced to the point of collapsing.<br />
<br />
-Out of all the life that ever existed, 31.4159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566072629339550548239557137256840232268213012476794522644820910235647752723082081063518899152692889108455571126603965034397896278250016110153235160519655904211844949907789992007329476905868577878720982901352956613978884860509786085957017731298155314951681467176959760994210036183559138777817698458758104466283998806006162298486169353373865787735983361613384133853684211978938900185295691967804554482858483701170967212535338758621582310133103877668272115726949518179589754693992642197915523385766231676275475703546994148929041301863861194391962838870543677743224276809132365449485366768000001065262485473055861598999140170769838548318875014293890899506854530765116803337322265175662207526951791442252808165171667766727930354851542040238174608923283917032754257508676551178593950027933895920576682789677644531840404185540104351348389531201326378369283580827193783126549617459970567450718332065034556644034490453627560011250184335607361222765949278393706478426456763388188075656121689605041611390390639601620221536849410926053876887148379895599991120991646464411918568277004574243434021672276445589330127781586869525069499364610175685060167145354315814801054588605645501332037586454858403240298717093480910556211671546848477803944756979804263180991756422809873998766973237695737015808068229045992123661689025962730430679316531149401764737693873514093361833216142802149763399189835484875625298752423873077559555955465196394401821840998412489826236737714672260616336432964063357281070788758164043814850188411431885988276944901193212968271588841338694346828590066640806314077757725705630729400492940302420498416565479736705485580445865720227637840466823379852827105784319753541795011347273625774080213476826045022851579795797647467022840999561601569108903845824502679265942055503958792298185264800706837650418365620945554346135134152570065974881916341359556719649654032187271602648593049039787489589066127250794828276938953521753621850796297785146188432719223223810158744450528665238022532843891375273845892384422535472653098171578447834215822327020690287232330053862163479885094695472004795231120150432932266282727632177908840087861480221475376578105819702226309717495072127248479478169572961423658595782090830733233560348465318730293026659645013718375428897557971449924654038681799213893469244741985097334626793321072686870768062639919361965044099542167627840914669856925715074315740793805323925239477557441591845821562518192155233709607483329234921034514626437449805596103307994145347784574699992128599999399612281615219314888769388022281083001986016549416542616968586788372609587745676182507275992950893180521872924610867639958916145855058397274209809097817293239301067663868240401113040247007350857828724627134946368531815469690466968693925472519413992914652423857762550047485295476814795467007050347999588867695016124972282040303995463278830695976249361510102436555352230690612949388599015734661023712235478911292547696176005047974928060721268039226911027772261025441492215765045081206771735712027180242968106203776578837166909109418074487814049075517820385653909910477594141321543284406250301802757169650820964273484146957263978842560084531214065935809041271135920041975985136254796160632288736181367373244506079244117639975974619383584574915988097667447093006546342423460634237474666080431701260052055928493695941434081468529815053947178900451835755154125223590590687264878635752541911288877371766374860276606349603536794702692322971868327717393236192007774522126247518698334951510198642698878471719396649769070825217423365662725928440620430214113719922785269984698847702323823840055655517889087661360130477098438611687052310553149162517283732728676007248172987637569816335415074608838663640693470437206688651275688266149730788657015685016918647488541679154596507234287730699853713904300266530783987763850323818215535597323530686043010675760838908627049841888595138091030423595782495143988590113185835840667472370297149785084145853085781339156270760356390763947311455495832266945702494139831634332378975955680856836297253867913275055542524491943589128405045226953812179131914513500993846311774017971512283785460116035955402864405902496466930707769055481028850208085800878115773817191741776017372216128524897425555516076371675054896173016809613803811914361143992106380050832140987604599309324851025168294467260666138151745712559754953580239983146982203613380828499356705575524712902745397762140493182014658008021566536067765508783804304134310591804606800834591136640834887408% of it are reincarnations of Gmaas.<br />
<br />
-Gmaas can make so many edits to this holy bible, that it would destroy the known universe.<br />
<br />
(Why is this a thing?) Because we are all worshippers of Gmaas. How dare you suggest such an atrocity?!?!?! You are now hereby banished from the holy bible of Gmaas and shall not make edits ever again! -Decreed by THE ENFORCER<br />
<br />
This article is NOT spam<br />
<br />
Gmaas is actually an AoPS site admin... (And a human) not a cat...<br />
<br />
All hail Gmaas!<br />
<br />
P.S. Gmaas one USAMO 5 times in a row. That's because he invented USAMO. When gmaas took it nobody knew about it and he was the only one who took it. So of course, he won. How dare you spell Gmaas with a lowercase G? He is the supreme and awesome ruler of the universe!<br />
<br />
P.P.S. Gmaas invented the word Yeet.<br />
P.P.P.S. Gmass is the first person who played the game YECK (Moth poth 2019 reference)</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=Gmaas&diff=109391Gmaas2019-08-26T18:47:10Z<p>Vsar0406: </p>
<hr />
<div>THEM FACTS ABOUT THE GREAT EPIC AWESOME GMAAS: EDIT: Words fail to describe the epic nature of Gmaas, for he is too almighty and powerful to be bound by the plebeian and trifling words. But even the Great Epic Awesome Plenipotentiary GMAAS cannot get rid of a language that's been around for a <math>100000000^{10000000000}</math> years and counting. That's older than he is. EDIT EDIT: This fact should be cited as fact 0. Zero is a natural number.<br />
<br />
1. Gmaas' theorem states that for any math problem, Gmaas knows the answer to it. This theorem was proved by Gmaas.<br />
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2. The GMATS were supposed to be called the GMAAS, but the manager, gmaas, wanted to eat some gnats. EDIT: Gmaas has stopped eating gnats because they taste <s>bad</s> dreadful.<br />
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3. Gmaas' archenemy is John Wick. EDIT: John Wick once gave Gmaas 31,415,926,535,897,932,384,626,433,832,795,028,841,971,693,993,751,058,209,749,445,923,078,164,062,862,089,986,280,348,253,421,170,679 Oren Berries, but Gmaas thought they were Oran Berries. That is why Gmaas hates John Wick. EDIT EDIT: Gmaas knew they were Oren Berries, because Gmaas knows everything, but he decided to play along. <br />
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4. Gmaas wants every fact to have a pi reference. Gmaas created pi.<br />
<br />
5. Gmaas owned many memes. Then they died. He left the meme business because others took it over. Gmaas decided to make some more memes after that. Since then, he has been working for the government. All of the pliticians are his henchmen. He controls the government. He wrote all of the laws and documents. <br />
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6. Gmaas owns Scratch. EDIT: Gmaas sued them because Scratch cat was supposed to be a picture of Gmaas. But this was one lawsuit he lost. EDIT EDIT: Gmaas won that lawsuit, but he ate food so he calmed down and dropped the case. <br />
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7. Thanos wishes he could be like Gmaas. It's why he got the Infinity Stones and snapped.<br />
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8. Gmaas dies in Endgame, but he somehow possesses Thanos and kills everyone. EDIT: Gmaas never dies. EDIT: Gmaas has the power to die whenever he wants and frequently does this to escape others' woes in life. Of course, he himself never faces such troubles.<br />
<br />
9. He hates contemporary music. He only like Renaissance music, Baroque music, Classical music, and Romantic music. EDIT: His only exception is Queen music(Especially Bohemian Rhapsody). EDIT EDIT: Gmaas also likes Debussy. EDIT EDIT EDIT: But he thinks rock'n'roll is awful.<br />
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10. Gmaas is superior to you. If you see Gmaas or a picture of the Great Gmaas, bow down. EDIT: It is proper to have a painting or lifesize sculpture of Gmaas. If you do not, Gmaas will put one of them there himself. EDIT EDIT: That is exactly why you should not have a statue of Gmaas: Gmaas will give you one for free. EDIT EDIT EDIT: A life size sculpture of Gmaas will be infinitely large, because that is how superior Gmaas is. Pictures also have power, so pictures require power to make. Making a sculpture of Gmaas will require almost an infinite amount of power. Only Gmaas can make a quality sculpture of himself, and if anyone makes a low quality sculpture of Gmaas, it will be disrespectful to such a superior power. Therefore, it is best to let Gmaas make a proper sculpture of himself, so he is respected. If you want to respect him the most, you should have a high quality sculpture of Gmaas.<br />
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11. Gmaas is known to barf entire universes at will. EDIT: Every once in a while, he barfs a furball, which always turns into a black hole. The less impressive ones turn into neutron stars.<br />
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12. Gmaas farted and created a false vacuum, but then he burped, destroying the false vacuum.<br />
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13. Gmaas was the first person to use the Infinity Gauntlet. EDIT: Gmaas created the Infinity Gauntlet and the Infinity Stones. EDIT EDIT: But Thanos stole them after Gmaas died for 0.31415926535 seconds.<br />
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14. Gmaas killed Thanos with a swat of Gmaas's tail. Gmaas barfed and created a furball, which lead to a new dimension, where he put a newly revived Thanos to become a farmer, when Thor aimed for the head. Gmaas got mad and made him fat.<br />
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15. Gmaas won an infinite amount of games against AlphaGo and Gary Kasparov while eating dinner.<br />
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16. Gmaas owns a pet: sseraj. Gmaas likes to play chess with his pets. EDIT: Gmaas has long moved on from chess because he was too good for it.<br />
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17. Gmaas is so interesting that an entire science has been devoted to studying him: Gmaasology.<br />
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18. Gmaas is the only known living being who has a PhD in Gmaasology.<br />
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19. Most universities, including Harvard, are beginning to offer MAs in Gmaasology.<br />
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20. Gmaasology is one of the most eminent fields of science, falling behind Physics, Biology, Chemistry, Economics, Geology, and Computer Programming.<br />
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21. Gmaas wants his AoPS Wiki page to be the longest ever. EDIT: Sadly, the Gmaas page is only the fourth longest page on AoPS wiki. It has around 50,000 bytes. EDIT EDIT: The Gmaas page is getting closer and closer! Gmaas has beaten Primitive Pythagorean Triple and Proofs without words and is the second longest AoPS Wiki page. It now has around 60,000 bytes. However, it will still be a challenger to overcome 2008 iTest Problems, which has around 73,000 bytes. EDIT EDIT EDIT: Gmaas has beaten 2008 iTest Problems! It is the longest AoPS Wiki article ever. Gmaas's article has 89,119 bytes.<br />
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22. Gmaas has the longest lifespan of any cat. He has lived for 3,141,592,653,589,793,238,462,643,383,279 years. (He is older than the universe.)<br />
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23. Gmaas is the ancient Greek god of cats and catfish.<br />
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24. Gmaas can turn things into gold. EDIT: Gmaas can turn anything into anything.<br />
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25. Gmaas can eat lava. EDIT: Everyone can eat lava once. After you eat it once, you die. EDIT EDIT: Gmaas can eat anything.<br />
<br />
26. Gmaas's Theorem states that Gmaas knows the answer to any math problem. EDIT: That theorem was proved by Gmaas. EDIT EDIT: Gmaas's Theorem has real world applications: because Gmaas knows the answer to any math problem, you can use Gmaas to solve math problems. Gmaas is busy, so he charges a fee of one dollar for 1,000,000 math problems. EDIT EDIT EDIT: The fee has gone up. It is now 1,000,000 dollars for one math problem. Gmaas's technician made a mistake and reciprocaled the fee.<br />
<br />
27. Gmaas can only be described as Gmaas. EDIT: Gmaas has an age, but his age changes all the time. Every second his age increases by one second.<br />
<br />
28. Gmaas should be capitalized to show respect. EDIT: It is normal to capitalize people's names. EDIT EDIT: Gmaas isn't a person, he is a divine entity that takes the form of a cat, and should therefore be worshipped.<br />
<br />
29. The steps to summon Gmaas can be found at Talk:Gmaas.<br />
<br />
30. Gmaas owns your AoPS account 31.4159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912% of the time. EDIT: There is an exception to this: Gmaas owns his own account 99.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999% of the time. The only time when Gmaas did not control his AoPS account was when he had slow internet. For Gmaas, "slow internet" happens when it takes more than a nanosecond to load a webpage. EDIT EDIT: Gmaas owns every AoPS account at some point.<br />
<br />
31. Everyone, except for me, is Gmaas. EDIT: You are also Gmaas. EDIT EDIT: Gmaas is not me nor you. EDIT EDIT EDIT: Gmaas is in us all and also not in us all. Why? The power of Gmaas. EDIT EDIT EDIT EDIT: Gmaas is an energy field created by all living things. It surrounds us and penetrates us. It binds the galaxy together.<br />
<br />
32. Gmaas used to be a dog, but he didn't like to be a dog. So he became a cat.<br />
<br />
33. Gmaas can be spotted in The Matrix at 31:41:59, metric time.<br />
<br />
34. The Metropolitan Museum of Art and the Louvre are Gmaas's private art collections from 3:14 AM to 3:15 AM. EDIT: The only exception was on the 3141th day after its opening. EDIT EDIT: All the paintings in these museums are secretly portraits of Gmaas in his most glorious human/animal forms.<br />
<br />
35. Gmaas is a Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is owned by Gmaas who is blah blah blah blah blah blah blah blah blah blah blah blah blah blah.<br />
<br />
36. Gmaas says hello. EDIT: Gmaas does not speak; he only uses mind signals. Speaking is too primitive for Gmaas.<br />
<br />
37. For one day, Gmaas was Richard Rusczyk, Gmaas, and David Patrick at the same time. It felt strange, so Gmaas stopped.<br />
<br />
38. Gmaas, in addition to being the oldest cat in history, the most powerful cat in history, and the most confusing cat in history, is also the largest cat in history.<br />
<br />
39. Gmaas is dead--he was eaten for lunch. EDIT: The above sentence is incorrect. Gmaas has not sent a gamma ray burst to destroy the planet, which has happened every time someone has eaten Gmaas.<br />
<br />
40. Gmaas is the creator of the BCPI Ai project.<br />
<br />
41. Gmaas exists in <math>2\pi^2</math> dimensions because he doesn't like string theory.<br />
<br />
42. Christmas was actually supposed to be called Gmaasmas. Until it wasn't.<br />
<br />
- <math>\pi</math> is a representation of how many pies Gmaas has eaten. EDIT: The number <math>\pi</math> was created by Gmaas. He took a ten-sided die and flipped it an infinite number of times. The numbers he rolled became the digits of <math>\pi</math>.<br />
<br />
- <math>e</math> is a representation of how many days Gmaas forgot to eat. EDIT: The number <math>e</math> was created by Gmaas. He took a book that has infinite pages and flipped to a random page. The digits of the page number became digits of <math>e</math>. EDIT EDIT: That is impossible. The previous fact would mean that <math>e</math> has a last digit, which it does not. EDIT EDIT EDIT: That is why Gmaas is still flipping to this day. EDIT EDIT EDIT EDIT: Why would he still be doing that? That would be boring. EDIT EDIT EDIT EDIT EDIT: Gmaas is not flipping the book now because he can flip an infinite amount of pages in <math>\frac{1}{\infty}</math> seconds. EDIT EDIT EDIT EDIT EDIT EDIT: Then why isn't he done? EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The power of Gmaas. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The editors of the Gmaas article like to make long chains of edits, don't we? EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Yes, we do. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: I do too. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: So do I. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The quantity of edits only verifies how high-quality this holy bible of Gmaas is, because with each edit, this bible becomes better. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: That is exactly why we are editing this. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: I will make one more edit, just to respect Gmaas.<br />
<br />
- Gmaas is the creator of everything including nothing. <br />
<br />
- According to recent DNA tests, famous historical people, such as Euclid, Julius Caesar, Omar Khayyam, George Washington, and Ramanujan are actually Gmaas in disguise. EDIT: Gmaas has been thousands of people; only 99.9% of them were important historical figures. EDIT EDIT: They aren't dead. They're still alive. EDIT EDIT EDIT: They are all dead reincarnations of Gmaas. Gmaas only has one reincarnation at a time. He is right now a cat living in sseraj's house. <br />
<br />
- Gmaas is a cat. EDIT: How many times do we say this? EDIT EDIT: Very many times. EDIT EDIT EDIT: Gmaas can be anything, but he chooses to be a cat. EDIT EDIT EDIT EDIT: He has been a human dozens of times. In fact, Gmaas painted the Lascaux cave paintings.<br />
<br />
- Gmaas has the following powers: trout, carp, earthworm, and catfish. Gmaas never uses any of them because Gmaas has an infinite number of powers. EDIT: Gmaas has used his catfish power several times. EDIT EDIT: Gmaas once used all his powers 3,141,592,653,589,793,238,462,643,383,279 times in 1 second.<br />
<br />
- Gmaas was once spotted in minecraft chewing a tree. EDIT: The tree broke. EDIT EDIT: Gmaas once broke a Nokia. EDIT EDIT EDIT: Gmaas can break anything except for Gmaas's logic. It is too strong. EDIT EDIT EDIT EDIT: Gmaas is strong.<br />
<br />
- Gmaas was spotted in Roblox eating a tacocat. EDIT: Tacocat is really just what happens when Gmaas sheds. Shedding is annoying for Gmaas, so he sheds no more. Therefore, there are only 271,828,182 tacocats in the world. EDIT EDIT: However, Tacocats reproduce, so they are not in danger of extinction.<br />
<br />
- Gmaas would like to go to Taco Bell, but Gmaas goes to Wendy's instead. No one knows why. EDIT: Because Taco Bell doesn't serve tacocats.<br />
<br />
- Gmaas real name is Grayson Maas. He is the CEO of AoPS. EDIT: Gmaas's real name is Gmaas. He is not the CEO of AoPS. EDIT EDIT: Gmaas has always been the master of AoPS as he is AoPS.<br />
<br />
- Gmaas has a pet pufferfish named Pafferfash. EDIT: He also has a goldfish named Sylgar.<br />
<br />
- Gmaas has colonized the universe. EDIT: Gmaas created the universe, so he is allowed to claim control over it. EDIT EDIT: Gmaas created every universe.<br />
<br />
- Some people think that Gmaas is a human. However, this has never been proven. Many AoPSers believe Gmaas is a cat. EDIT: Gmaas is a cat. EDIT EDIT: Yeah, we've said that already. EDIT EDIT EDIT: It does not matter how many times we say it; it will always be true. EDIT EDIT EDIT EDIT: Gmaas is a cat. EDIT EDIT EDIT EDIT EDIT: Right now he is a cat, but many of his lives have been other species. EDIT EDIT EDIT EDIT EDIT EDIT: He has been a dog, as said before, but it was too boring.<br />
<br />
- Gmaas started pastafarianism. But then converted to Catholicism because Gmaas knows all EDIT: In that religion, one can only eat pasta.<br />
<br />
- Gmaas could eat your hand, but he would not because hands taste bad.<br />
<br />
- According to the Interuniversal Gmaas Society, 17.548 percent of universe's population thinks that Gmaas is spelled "Gmass". EDIT: In case you don't know already, the name Gmass is spelled Gmaas. Alternative spellings include GMAAS, gmaas, gmaas, Gmaas, Gmail, Maas, G. Maas, G. Mass, Gabriel Maas, Genius of Maas, General Maas, Greek Mass, and the big fluffy kitty who lives in sseraj's house. These are no longer accepted spellings, and Gmaas is the current acceptable spelling.<br />
<br />
- The Interuniversal Gmaas Society was founded in 1314 on May 9th at 2:06:53 PM. EDIT: Ever since then, Gmaas day has been celebrated on May 9th.<br />
<br />
- The Interuniversal Gmaas Society has just reconstruct a lost book about Gmaas from Lucretius's De Rerum Natura. They researched this for three years. EDIT: A few years ago the Society compiled a biography of Gmaas's last twenty lives. EDIT EDIT: The only copies of these biographies are locked in the Gmaasian Library beneath the Library of Congress. EDIT EDIT EDIT: See the Gmaasology page for more information on these projects and others made by the Interuniversal Gmaas Society.<br />
<br />
- The Interuniversal Gmaas society has found out all of the information and more. For details on the history of the Interuniversal Gmaas Society, see the Gmaathamatics page.<br />
<br />
- Gmaas likes to surprise unsuspecting people.<br />
<br />
- Gmaas loves sparkly mechanical pencils. EDIT: Gmaas has eaten several mechanical pencils. EDIT EDIT: He absorbed them and became colorful for 0.271828182846 seconds.<br />
<br />
- This page is Gmaas's holy book where people go to worship Gmaas in Maas. EDIT: This is an unusual holy where everyone edits it. EDIT EDIT: That is the point. Gmaas is too lazy to write or to hire someone to write his own holy book, so he lets people write it for free. EDIT EDIT EDIT: Gmaas does not like being called lazy. Our language is simply too unimportant for him to waste time on.<br />
<br />
- Gmaas tastes like a furry meatball. EDIT: No one has ever tasted Gmaas's sacred body before. EDIT EDIT: Once, he was a catfish, and someone ate him for dinner. Gmaas was angry and the entire planet exploded. (This was on the planet Demeter. It blew up into so many pieces that the Asteroid Belt was formed. The biggest asteroid in the belt is called Ceres, the Roman version of Demeter, in honor of the lost planet.)<br />
<br />
- Gmaas's favorite food is pepperoni pizza. EDIT: Gmaas's favorite food is turnips. EDIT EDIT: Gmaas hates catnip and turnips, and pepperoni. He only likes alien alienish H2So4. EDIT EDIT EDIT: He does love turnips. He has a secret turnip garden under sseraj's house.<br />
<br />
- Gmaas is Johnny Johnny's Papa. EDIT: We'll never know. EDIT EDIT: Gmaas caught Johnny Johnny eating sugar and lying. He is Johnny Johnny's Papa.<br />
<br />
- Gmaas is in you, and Gmaas is in you, and Gmaas is in me. EDIT: Gmaas is in all cats. EDIT EDIT: He is not in every cat. The Guinness Book of World Records has a cat that does not have any Gmaas. EDIT EDIT EDIT: Gmaas invented The Guinness Book of World Records. EDIT EDIT EDIT EDIT: Gmaas invented the world. EDIT EDIT EDIT EDIT EDIT: Gmaas will also destroy the world.<br />
<br />
- Gmaas always remembers not to destroy the universe. EDIT: Once he forgot and had to travel back in time to stop it.<br />
<br />
- Gmaas created many user's accounts. EDIT: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058% of accounts on AoPS are Gmaas in disguise.<br />
<br />
- Gmaas is both living and nonliving. EDIT: He is living 90% of the time. Every once in a while he takes a break and dies.<br />
<br />
- Gmaas is quasiomnipotent. He cannot comprehend the stupidity of humans.<br />
<br />
- All hail the Gmaas cloud! EDIT: Gmaas is a cloud: a cloud of electrons and nuclei.<br />
<br />
- Some things are beyond possible human comprehension. Nothing is beyond Gmaas. EDIT: The only thing beyond Gmaas is his tail; he has never managed to eat it. EDIT EDIT: Once he ate it. It tasted bad, so he didn't ever eat it again.<br />
<br />
- Gmaas eats food and resides at King Arthur's throne when he feels like it. EDIT: King Arthur is dead. However, Welsh folk stories say that he will come back if the Welsh people are in trouble. EDIT EDIT: King Arthur lives on paper flour bags. He came back when the Welsh people didn't have enough bread.<br />
<br />
- Gmaas owns a rabbit. EDIT: Gmaas ate it on March 19, 2019. It reincarnated on the other side of the planet. EDIT EDIT: Gmaas ate it again on April 31, 2019.<br />
<br />
- Gmaas is both singular and plural. EDIT: It is usually singular. EDIT EDIT: The plural of Gmaas in English and in Latin is Gmaases. (Gmaas is a third declension noun: Gmaas, Gmaasis, m.)<br />
<br />
- Gmaas eats disbelievers as if they were donuts for breakfast. (Yet I'm somehow still alive. Do you think Gmaas actually ate my soul?) EDIT: Yes, I do. Gmaas is just typing through your account. EDIT EDIT: Gmaas typed through everyone's account. EDIT EDIT EDIT: Gmaas owns most AoPSers, including me. So that's why I'm typing.<br />
<br />
- Gmaas knows Jon Snow's parents. EDIT: Gmaas was Jon Snow's parents for 0.3141592653589793238 seconds, but it felt weird. So he became Gmaas again.<br />
<br />
- All Gmaas article editors will be escorted to Gmaas heaven after they die. EDIT: I hope so because I edited this article. EDIT EDIT: Me too.<br />
<br />
- Gmaas won all the wars. EDIT: He did not win the Intergmaasian War, which was between Gmaas's head and his tail. His tail won. Two flees died in the war. EDIT EDIT: Stefán Karl Stefansson died in the war, which made Gmaas very sad. Because of this, Gmaas<br />
started the world peace movement.<br />
<br />
- Gmail was named after Gmaas. EDIT: Google was named after Gmaas. EDIT EDIT: Almost every word starting with G is named after Gmaas.<br />
<br />
- Gmaas ate cat-food today. EDIT: Gmaas also ate it yesterday. EDIT EDIT: Only because there was no alien alienish H2So4.<br />
<br />
- Gmaas won Battle For Dream Island and Total Drama Island. EDIT: Gmaas made Dream Island. And he ate it. It tasted like dirt.<br />
<br />
- Somehow Gmaas exists at all places at the same time. EDIT: Gmaas does not exist in my kitchen. EDIT EDIT: I'll just go check. Aaaaaaaaah! He is in my kitchen. He is eating everything! He sees me! I am dyingiuhbjhjucbfwiknjfwvkjwfvnkfvw<br />
<br />
- Gmaas can lift with Gmaas's will. EDIT: Gmaas can lift with no one's will while he is sleepwalking.<br />
<br />
- Gmaas is the rightful heir to the Iron Throne. EDIT: Gmaas made the Iron Throne.<br />
<br />
- Gmaas is actually Teemo in League of Legends because Gmaas made LoL and they made a honorary Gmaas character.<br />
<br />
- Gmaas started the Game of Thrones. EDIT: Gmaas will end the Game of Thrones.<br />
<br />
- Gmaas has killed himself hundreds of times. He was reincarnated as a different species each time. EDIT: Gmaas has only died two times. Other times he was putting on a magic show. The kids were very impressed. EDIT EDIT: Gmaas has died and reincarnated thousands of times.<br />
<br />
- Gmaas created everything after puking. EDIT: He could not have puked because he is a god. Gods do not do that. EDIT EDIT: Gmaas does that. EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gordan's last name was named after Gmaas. EDIT: But Gmaas did not want people disrupting his beauty sleep. So he changed it.<br />
<br />
- Gmaas is more powerful than Gohan.<br />
<br />
- Gmaas is over 90000 years old. EDIT: Gmaas is trillions of years old.<br />
<br />
- Gmaas has 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 cat lives, maybe even more. Gmaas has 0 dog lives. EDIT: He has 314,159,265 fish lives. EDIT EDIT: Out of Gmaas's 314,159,265 fish lives, 271,828,182 are catfish lives. He has used up 141,421,356 of them. EDIT EDIT EDIT: Gmaas has infinitely lives of all types. EDIT EDIT EDIT EDIT: How? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Who wrote Harry Potter? None other than Gmaas himself. EDIT: That is incorrect. EDIT EDIT: The above post is irrelevant. Gmaas created J K Rowling. Therefore, he created Harry Potter. EDIT EDIT EDIT: Gmaas has strong logic. No one can break it. Not even Gmaas himself. He is still trying to this day.<br />
<br />
- Gmaas created the catfish. EDIT: See a few posts above for more information about Gmaas and catfish.<br />
<br />
- Gmaas has proven that the universe is infinite by traveling to the edge of the universe in a second. EDIT: He has never repeated this experiment because Gmaas is busy and has better things to do.<br />
<br />
- Gmaas founded Target, but then Gmaas sued them for making the mascot look like a dog when it was supposed to look like Gmaas. EDIT: They went broke because Gmaas sued them but then Gmaas ate a fudge popsicle that made him super hyper and he made Target not broke anymore in his hyperness.<br />
<br />
- Everyone has a bit of Gmaas inside them. EDIT: I don't. EDIT EDIT: Yes, you do.<br />
<br />
- Gmaas likes to eat popsicles. Especially the fudge ones that get him hyper. EDIT: Gmaas is a popsicle. EDIT EDIT: Then how come Gmaas hasn't melted? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- When Gmaas is hyper, he runs across Washington D.C. and grabs unsuspecting pedestrians, steals their phones, hacks into them, and downloads PubG onto their phone.<br />
<br />
- Gmaas's favorite cereal is fruit loops. Gmaas thinks it tastes like unicorns jumping on rainbows. EDIT: Gmaas eats unicorns jumping on rainbows like a toddler eats Goldfish.<br />
<br />
- Gmaas thinks that the McChicken has too much mayonnaise. EDIT: Gmaas thinks McDonald's is not good enough for him.<br />
<br />
- Gmaas is a champion pillow-fighter. EDIT: Gmaas invented pillows.<br />
<br />
- Gmaas colonized Mars. EDIT: Gmaas also colonized Jupiter, Pluto, and several other galaxies. Gmaas cloned little Gmaas robots (with Gmaas's amazingly robotic skill of coding) and put them all over a galaxy called Gmaasalaxy. EDIT EDIT: Gmaas has colonized the whole universe.<br />
<br />
- Gmaas has the ability to make every device play "The Duck Song" at will. EDIT: "The Duck Song" was copied off of the "Gmaas song," but the animators though Gmaas wasn't catchy enough.<br />
<br />
- Gmaas once caught the red dot and ate it. EDIT: Gmaas is a red dot.<br />
<br />
- Gmaas's favorite color is Gmaasian blue, a very rare blue that shines with the brightness of lightning. EDIT: it's <math>1000^1000x</math> brighter than lightning. Gmaasian blue occurs when a meteor hits the earth and usually is only seen for a few seconds. Only Gmaas has good enough eyesight to see it for that short a time. <br />
<br />
- Gmaas can create wormholes and false vacuums. EDIT: He is made out of exotic matter.<br />
<br />
- Gmaas is a champion pvp Minecraft player.<br />
<br />
- Gmaas is the coach of True Ninja Music and Myth.<br />
<br />
- Gmaas caught a CP 6000 Mewtwo with a normal Pokeball in Pokemon Go.<br />
<br />
- Gmaas founded Costco.<br />
<br />
- Gmaas does not need to attend the FIFA World Cup. If Gmaas did, he would start the game with a goal and break the ankles of everyone watching the World Cup, including you, at the same time in a fraction of a second, even if you are watching from a device. EDIT: Gmaas created your device. EDIT EDIT: Gmaas is your device.<br />
<br />
- Gmaas can solve any puzzle instantly except for the 3x3 Rubik's Cube. EDIT: When Gmaas is handed a 3x3 Rubik's Cube, it is always already solved. Why? The power of Gmaas.<br />
<br />
- Gmaas caught a CP 20,000 Mewtwo with a normal Pokeball and no berries blindfolded first try in Pokemon Go.<br />
<br />
- When Gmaas flips coins, they always land tails, except when Gmaas makes bets with Zeus.<br />
<br />
- On Gmaas's math tests, Gmaas always gets <math>\infty</math>. EDIT: He gets a 26 on the AMC8 every year. The results never show him because Gmaas is no longer in middle school.<br />
<br />
- Gmaas's favorite number is <math>\pi</math>. It is also one of Gmaas's favorite foods. EDIT: Gmaas created <math>\pi</math>, as well as most other constants, such as <math>e</math> and <math>\sqrt{2}</math>.<br />
<br />
- Gmaas's burps created all gaseous planets.<br />
<br />
- Gmaas beat Luke Robatille in an epic showdown of catnip consumption.<br />
<br />
- Gmaas's wealth is unknown, but it is estimated to be more than Scrooge's. EDIT: It may be more than John D. Rockefeller. EDIT EDIT: More accurate estimates predict that Gmaas's wealth is infinite.<br />
<br />
- Gmaas has a summer house on Mars. EDIT: Gmaas has a fall house on Venus. EDIT EDIT: Gmaas has a winter house on Jupiter. EDIT EDIT EDIT: Gmaas has a spring house on Earth. EDIT EDIT EDIT EDIT: Gmaas also experiences a fifth season called wintrautumn. It happens during November and December and is the cross between fall and winter. Everything is dreary, but there is no snow. Gmaas spends wintrautumn in his house on Venus, where he is incinerated daily. He reincarnates every night through the power of Gmaas. EDIT EDIT EDIT EDIT EDIT: Gmaas invented a new season on Feb. 31, 2019 called wintrsummer. It is spring but transcends spring.<br />
<br />
- The Earth and all known planets are Gmaas's hairballs.<br />
<br />
- Gmaas attended Harvard, Yale, Stanford, MIT, UC Berkeley, Princeton, Columbia, and Caltech at the same time using a time-turner.<br />
<br />
- Gmaas attended Hogwarts and was a prefect. EDIT: Gmaas is headmaster. EDIT EDIT: Hogwarts was supposed to be called Hogmaas.<br />
<br />
- Mrs. Norris is Gmaas's archenemy. Gmaas yawned, and Ms. Norris was petrified. EDIT: Gmaas is the basilisk, and he let Harry Potter pet him. Harry did not kill the basilisk, he only gave Gmaas a haircut. EDIT EDIT: Gmaas hates having a haircuts, so he reincarnated Voldemort to punish Harry.<br />
<br />
- Gmaas is a demigod and attends Camp Half-Blood over summer. Gmaas is the counselor for the Apollo cabin because cats can be demigod counselors too. EDIT: Apollo was one of the many reincarnations of Gmaas.<br />
<br />
- Gmaas has completed over 2,000 quests and is very popular throughout Camp Half-Blood. Gmaas has also been to Camp Jupiter. EDIT: Gmaas is Camp Jupiter, he is also Camp Half-Blood. EDIT EDIT: How? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Percy Jackson was only able to complete his quests because Gmaas helped him. EDIT: Gmaas is Percy Jackson. In fact, you are Gmaas, but Gmaas is not you.<br />
<br />
- Gmaas painted the Mona Lisa, The Last Supper, and A Starry Night. EDIT: Gmaas knows that their real names are Gmaasa Lisa, The Last Domestic Meal, and Far-away Light.<br />
<br />
- Gmaas knows that the Blood Moon is just the red dot. He has not caught it yet. EDIT: He caught it during the super blue blood moon.<br />
<br />
- Gmaas attended all the Ivy Leagues.<br />
<br />
- I am Gmaas. EDIT: No you are not. You only have part of Gmaas inside of you. EDIT EDIT: I am also Gmaas. EDIT EDIT EDIT: But it is I who am Gmaas. EDIT EDIT EDIT EDIT: Gmaas is in us all. EDIT EDIT EDIT EDIT EDIT: Gmaas is all of us yet none of us. EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas is a cat. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: He is only in a cat form right now. He can be whatever he wants to be. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: This chain of edits has superseded another chain of edits on this page for the record of longest chain of edits on AoPS Wiki. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: But the edits in this chain tend to be shorter than most. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: You're right. But we sure do love strings of edits, don't we? EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas makes the edits. He is in your head spinning edits in your brain. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas is made to be edited. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Gmaas pays people to edit. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: Some people edit even without Gmaas's payment. They do it because they are believers.<br />
<br />
- In 2018 Gmaas once challenged Magnus Carlsen to a chess game. Gmaas won every round. EDIT: Gmaas ate the chess pieces afterwards. They tasted funny.<br />
<br />
- Gmaas was captured in 2017 but was released due to sympathy. EDIT: Gmaas was only captured in his concrete form; his abstract form cannot be processed by a feeble human brain.<br />
<br />
- Gmaas's fur is white, black, grey, yellow, red, blue, green, brown, pink, orange, turquoise, and purple at the same time. EDIT: Gmaas can make his fur any color he wants. EDIT EDIT: Gmaas's fur color can be ultraviolet.<br />
<br />
- Gmaas crossed the event horizon of a black hole and ended up in the AoPS universe.<br />
<br />
- Gmaas crossed the Delaware River with Washington. EDIT: Gmaas also crossed the Atlantic with the pilgrims.<br />
<br />
- If you are able to capture a Gmaas hair, Gmaas will give you some of his Gmaas power. EDIT: Gmaas does not shed and will eat anyone who has Gmaas hair. EDIT EDIT: Gmaas used to shed. The sheddings became tacocats.<br />
<br />
- Chuck Norris makes Gmaas jokes. EDIT: Those jokes all praise Gmaas.<br />
<br />
- Gmaas is also the ruler of Oceania, Eastasia, and Eurasia. EDIT: Gmaas wrote the book "1984."<br />
<br />
- Gmaas killed Big Brother by farting on him. Though Gmaas was caught by the Ministry of Love, Gmaas escaped easily. EDIT: Gmaas used to be Big Brother. EDIT EDIT: Gmaas destroyed the Ministry of Love.<br />
<br />
- Gmaas was not affected by Thanos's snap; in fact Gmaas is the creator of the Infinity Stones. EDIT: Gmaas is Thanos.<br />
<br />
- Everyone knows that Gmaas is a god. EDIT: That is because he is a god.<br />
<br />
- Gmaas also owns Animal Farm. Napoleon was Gmaas's servant. EDIT: Napoleon was Gmaas's slave.<br />
<br />
- Gmaas is the only person who knows where Amelia Earhart is. EDIT: Gmaas! Please tell us! It would be a great contribution to historical knowledge! EDIT EDIT: Gmaas responds, "No."<br />
<br />
- Gmaas is the only cat that has been proven transcendental. EDIT: Gmaas has been proved to be normal as well.<br />
<br />
- Grumpy cat reads Gmaas memes. EDIT: Grumpy cat then steals them and claims they're his. Gmaas isn't very happy about that, either. EDIT EDIT: That is why he looks grumpy in the memes.<br />
<br />
- The reason why AIME cutoffs aren't out yet is that Gmaas refused to grade them due to too much problem misplacement. EDIT: Gmaas controls the MAA. EDIT EDIT: Gmaas founded the MAA. EDIT EDIT EDIT: Gmaas is the MAA.<br />
<br />
- Gmaas dueled Grumpy Cat and won. Gmaas wasn't trying. EDIT: Gmaas killed Grumpy cat. EDIT EDIT: Gmaas revived Grumpy cat because he has not other rival.<br />
<br />
- Gmaas sits on the statue of Pallas and says forevermore. EDIT: When Gmaas was a statue, people hid him in a basement and forgot about him. Then civilization collapsed and the Middle Ages began. People finally discovered and melted down the statue of Gmaas around 1350 to make a church bell. Gmaas was free and reincarnated again, bringing about the Renaissance. EDIT EDIT: Despite the efforts of the recently founded National Gmatthematical Society of Florence, the statue was melted down. For more information about the National Gmatthematical Society of Florence, see the Gmaasology page.<br />
<br />
- Gmaas is a big fan of Edgar Allan Poe because he is actually Poe. EDIT: He became Poe during his thirty-year depression in the 19th century.<br />
<br />
- Gmaas does merely not use USD; he owns it.<br />
<br />
- In 2003, Gmaas used elliptical curves to force his reign over AoPS.<br />
<br />
- "Actually, my name is spelled "GMAAS"." (Citation needed)<br />
<br />
- Gmaas is Link in the Legend of Zelda. He despises Calamity Ganon in Breath of the Wild. "Too much of a hog..."<br />
<br />
- Gmaas is the smartest living being in the universe. EDIT: Notice how this sentences says "living being," so Gmaas might be dummer than some dead person. EDIT EDIT: Gmaas is the smartest being that has lived, lives, and will live. EDIT EDIT EDIT: How? EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas helped Sun Wukong on the Journey to the West.<br />
<br />
- Gmaas was the creator of Wikipedia.<br />
<br />
- Gmaas can hack any website he desires. EDIT: He can edit any website with the words Gmaas in it. EDIT EDIT: AoPS includes the word Gmaas right here, so Gmaas can hack it. EDIT EDIT EDIT: Gmaas can edit any website he desires.<br />
<br />
- Gmaas is the basis of Greek and Egyptian mythology. EDIT: He is also the basis for Aztec mythology. He once had a craving for human flesh, so he created human sacrifice.<br />
<br />
- Gmaas once sold Google to a man for around 12 dollars! EDIT: Gmaas has not spent those 12 dollars and is waiting for the economy to crash. EDIT EDIT: Why would he do that? EDIT EDIT EDIT: The power of Gmaas. EDIT EDIT EDIT EDIT: Gmaas is smarter than you think he is. Do you think you know how smart Gmaas is now? If so, then you are still wrong.<br />
<br />
- Gmaas uses a HP printer. It is specifically a HP 21414144124124142141414412412414214141441241241421414144124124142141414412412414 printer.<br />
<br />
- Gmaas owns all AoPS staff including Richard Rusczyk. EDIT: Richard Rusczyk is one of Gmaas's many code names.<br />
<br />
- Gmaas saw Yoda's birth. EDIT: Gmaas was Yoda's father. EDIT EDIT: Was Gmaas green like Yoda back then? EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas's true number of lives left is unknown; however, Gmaas recently confirmed that he had at least one left. Why doesn't Gmaas have so many more lives than other cats? The power of Gmaas. EDIT: This is all not true. EDIT EDIT: This is all true. EDIT EDIT EDIT: Gmaas has an infinite number of lives. EDIT EDIT EDIT EDIT: Gmaas does not have an infinite number of lives. He just has an unlimited number of lives.<br />
<br />
- sseraj once spelled Gmaas as gmASS by accident in Introduction to Geometry (1532). sseraj’s life was never the same afterwards. EDIT: Gmaas created sseraj. He is a Gmaas, but without the face, body, legs, and tail.<br />
<br />
- Gmaas has beaten Chuck Norris, The Rock, and John Cena all together in a fight.<br />
<br />
- Gmaas is a South Korean, North Korean, Palestinian, Israeli, U.S., Soviet, Russian, and Chinese citizen at the same time. EDIT: Gmaas is a citizen of every country in the world. Gmaas seems to enjoy the country of AoPS best, however.<br />
<br />
- "I am sand" destroyed Gmaas in FTW. EDIT: Because Gmaas accidentally died, he defeated "I am sand" 3,141,592,653 times after.<br />
<br />
- sseraj posted a picture of Gmaas with a game controller in Introduction to Geometry (1532).<br />
<br />
- Gmaas plays Roblox mobile edition and likes Minecraft, Candy Crush, and Club Penguin Rewritten. He also loves Catch that fish.<br />
<br />
- Gmaas is Roy Moore's horse in the shape of a cat.<br />
<br />
- Gmaas is a known roblox/club penguin rewritten player and is a legend at it. He has over <math>289547987693</math> roblox and <math>190348</math> in CPR.<br />
<br />
- This is all hypothetical. EDIT: This is all factual. For reference, see an earlier post.<br />
<br />
- Gmaas's real name is Princess. He has a sibling named Rusty/Fireheart/Firestar. EDIT: That is incorrect. Gmaas's real name is Gmaas.<br />
<br />
- Gmaas is capable of salmon powers. EDIT: Gmaas is capable of everything. Nothing is beyond Gmaas.<br />
<br />
- Gmaas told Richard Rusczyk to make AoPS.<br />
<br />
- The Gmaas is everything. Yes, you are part of the Gmaas-Dw789. EDIT: Gmaas is older than the universe. He is more than everything.<br />
<br />
- The Gmaas knows every dimension up to 99999999999999999999999999999999999999999999999999999999999999999999999999999999999th dimension. EDIT: He is working on the higher dimensions presently. It takes up 1% of his time. He spends the remaining 99% of his time eating, sleeping, and being. EDIT EDIT: Does that mean he stops being while he learns higher dimensions? EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT: Why? EDIT EDIT EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas went into a black hole and exited the white hole. He ended up in the 15th dimension where people drink tea every day. He stole 31,415,926,535,897,932,384,626,433,832,795,028,841,971,693,993,751,058,209,749,445,923,078,164,062,862,089,986,280,348,253,421,170,679,821,480,865,132,823,066,470,938,446,095,505,822,317,253,594,081,284,811,174,502,841,027,019,385,211,055,596,446,229,489,549,303,819,644,288,109,756,659,334,461,284,756,482,337,867,831,652,712,019,091,456,485,669,234,603,486,104,543,266,482,133,936,072,602,491,412,737,245,870,066,063,155,881,748,815,209,209,628,292,540,917,153,643,678,925,903,600,113,305,305,488,204,665,213,841,469,519,415,116,094,330,572,703,657,595,919,530,921,861,173,819,326,117,931,051,185,480,744,623,799,627,495,673,518,857,527,248,912,279,381,830,119,491,298,336,733,624,406,566,430,860,213,949,463,952,247,371,907,021,798,609,437,027,705,392,171,762,931,767,523,846,748,184,676,694,051,320,005,681,271,452,635,608,277,857,713,427,577,896,091,736,371,787,214,684,409,012,249,534,301,465,495,853,710,507,922,796,892 buckets of tea.<br />
<br />
- Gmaas is "TIRED OF PEOPLE ADDING TO HIS PAGE!!" (Maas 45). EDIT: This is Gmaas's holy, so he wants to have a longer version. For reference, see Maas 3,141,592,653,589,793,238,462. Gmaas is too lazy to write this book himself or to hire someone to do this for him, so he has assembled a group of unpaid freelancers on AoPS to write his holy book for him. He is watching it grow. However, Gmaas sometimes sees a comment that he does not like on the Gmaas article. He possesses an editor of Gmaas and makes him/her delete it. EDIT EDIT: AoPS itself is just an elaborately concealed piece of Gmaas propaganda. EDIT EDIT EDIT: How dare you reveal the truth! *Zaps previous editor out of existence* Now, where were we...<br />
<br />
- Gmaas is a Gmaas who is actually Gmaas. EDIT: Gmaas is omnipotent and omniscient. However, he is not always benevolent.<br />
<br />
- Gmaas has a penguin servant who runs GMAASINC. The penguin may or may not be dead. He had another penguin, who is mostly alive.<br />
- Gmaas owns a TARDIS, and can sometimes be seen traveling to other times for reasons unknown.<br />
<br />
- Gmaas knows how to hack into top secret AoPS community pages. EDIT: AoPS is just Gmaas's elaborately-concealed blog.<br />
<br />
- Gmaas used to be river clan cat who crossed the event horizon of a black hole and came out the other end. EDIT: He eventually created sseraj and has lived with sseraj ever since.<br />
<br />
- Gmaas is king of the first men, the anduls.<br />
<br />
- Gmaas is a well known professor at Meowston Academy. EDIT: He is professor of Gmaasology there. EDIT EDIT: Gmaas founded Meowston Academy. EDIT EDIT EDIT: It is actually called Gmaaston Academy<br />
<br />
- Gmaas comes from Gmaas Land, a magical place where pie is infinite and everything starts with a g<br />
<br />
- Gmaas is the CEO of Caterpillar.<br />
<br />
- Gmaas drinks at Starbucks everyday.<br />
<br />
- Gmaas is addicted to tuna, along with other more potent fish, such as salmon and trout.<br />
<br />
- Gmaas likes turning into fish and catching himself. EDIT: So far, Gmaas has spent 2,718,281 of his many lives as a catfish. However, sometimes, he has been catched as a catfish by other people. Luckily, Gmaas has always escaped.<br />
<br />
- Gmaas won the reward of being cutest and fattest cat ever--he surpassed grumpy cat. (He also out-grumped grumpy cat!!!) EDIT: He is in the Guinness Book of World Records for fluffiest cat ever.<br />
<br />
- He was last sighted at 1665 Alligator Swamp-A 4/1/18 at 3:14:15.92653589793238462 PM.<br />
<br />
- Gmaas is the owner of sseraj, not his pet. EDIT: Gmaas also created sseraj.<br />
<br />
- Gmaas is the embodiment of life, the universe, and beyond.<br />
<br />
- Gmaas watches memes about Gmaas. EDIT: All memes originate with Gmaas, but they are often posted by others.<br />
<br />
- After death Gmaas became the god of hyperdeath and obtained over 9000 souls.<br />
<br />
- One of Gmaas's many real names is Pablo Diego José Francisco de Paula Juan Nepomuceno María de los Remedios Cipriano de la Santísima Trinidad Ruiz y Picasso.<br />
<br />
- Gmaas is a certified Slytherin.<br />
<br />
- Gmaas once slept on sseraj's private water bed, so sseraj locked him in the bathroom. EDIT: Gmaas has superpowers that allowed him to overcome the horrors of Mr. Toilet while locked in the bathroom.<br />
<br />
- Gmaas once sat on an orange on a pile of AoPS books, causing an orange flavored equation explosion.<br />
<br />
- Gmaas conquered the moon and imprinted his face on it until asteroids came and erased it.<br />
<br />
- Gmaas is a supreme overlord who must be given <cmath>1000^{1,000,000,000,000,000,000,000^{1,000,000,000,000,000,000,000}}</cmath> minecraft diamonds. EDIT: Gmaas owns Mojang, but Gmaas sued them when it was supposed to be called Gmaascraft.<br />
<br />
- Gmaas is the Doctor Who lord, sports Dalek-painted cars, and eats human finger cheese, custard, and black holes. EDIT: Gmaas once ate a white hole. Gmaas then exploded and made a new universe.<br />
<br />
- Gmaas is everyone's favorite animal.<br />
<br />
- Gmaas is a Persian Smoke.<br />
<br />
- Gmaas lives with sseraj.<br />
<br />
- Gmaas dislikes geometry but enjoys number theory. EDIT: sseraj once posted a picture of Gmaas being grumpy after seeing an olympiad geometry problem.<br />
<br />
- Gmaas is often overfed (with probability <math>\frac{3972}{7891}</math>), or malnourished (with probability <math>\frac{3919}{7891}</math>) by sseraj. EDIT: Gmaas does not need food. He just eats food because it tastes good.<br />
<br />
- Gmaas has <cmath>\sum_{k=1}^{267795} [k(k+1)]+GMAAS+GMAAAAAAAAAAS</cmath> supercars, excluding the Purrari and the 138838383 Teslas.<br />
<br />
- Gmaas employs AoPS. EDIT: Gmaas is the reason why AoPS exists. EDIT EDIT: Gmaas is the reason why everything exists.<br />
<br />
- Gmaas is a Gmaas with yellow fur and white hypnotizing eyes. EDIT: His fur is not always yellow. His fur can be whatever color he chooses it to be.<br />
<br />
- Gmaas has the ability to divide by zero. EDIT: Gmaas knows what 1/0 is. What is it? We'll never know. EDIT EDIT: 1/0 = 0. How? The power of Gmaas.<br />
<br />
- Gmaas was born with a tail that is a completely different color from the rest of his fur. EDIT: Gmaas can change the color of his fur.<br />
<br />
- Gmaas's stare is very hypnotizing and effective at getting table scraps. EDIT: Gmaas's stare turned Medusa into rock, King Midas into gold, and sseraj into sseraj.<br />
<br />
- Gmaas always appears several minutes before certain classes start as an administrator. EDIT: This is becoming more and more infrequent. Sadly, sseraj rarely posts pictures of Gmaas before classes anymore. EDIT EDIT: Why is this happening? EDIT EDIT EDIT: The power of Gmaas.<br />
<br />
- Gmaas is an AoPS administrator under the alias Grayson Maas. EDIT: Gmaas always posts class surveys. He has a fake photo on his bio and has a real one on his community page. However, Gmaas himself has not yet posted on the Gmaas forum. EDIT EDIT: He also has not edited the Gmaas article, the Talk: Gmaas article, the Gmaasology article, or the sseraj article. EDIT EDIT EDIT: The final one is surprising because Gmaas knows more about sseraj than even sseraj does.<br />
<br />
- Gmaas died from too many Rubik's cubes in an Introduction to Algebra A class, but he was revived by the Dark Lord at 12:13:37 AM the next day. EDIT: This was thanks in return for Gmaas reincarnating him during the Triumverate Tournament.<br />
<br />
- It is uncertain whether or not Gmaas is a cat or is merely some sort of beast that has chosen to take the form of a cat (specifically a Persian Smoke). EDIT: He is both. EDIT EDIT: Actually, Gmaas is a cat. Gmaas said so, and science says so. EDIT EDIT EDIT: The profile for Gmaas on the list of AoPS teachers does not mention him being a cat. EDIT EDIT EDIT EDIT: The above post is irrelevant. Gmaas hides his identity under the alias Grayson Maas. EDIT EDIT EDIT EDIT EDIT: Gmaas us everything yet nothing. EDIT EDIT EDIT EDIT EDIT EDIT: How is that? The power of Gmaas.<br />
<br />
- Gmaas is distant relative of the chair of the department of Gmaasology at Princeton. EDIT: In the last few years, many universities have been opening Gmaasology departments. For more information, see the Gmaasology page.<br />
<br />
- Gmaas cannot be Force choked. Darth Vader learned that the hard way...<br />
<br />
- Gmaas is famous, and mods always talk about him before class starts.<br />
<br />
- Gmaas's favorite food is AoPS textbooks because they help him digest problems. EDIT: Gmaas wrote all AoPS textbooks but is never listed in the acknowledgments section.<br />
<br />
- Gmaas tends to reside in sseraj's fridge. EDIT: Gmaas once ate all sseraj's fridge food, so sseraj had to put him in the freezer. EDIT EDIT: Gmaas's fur can protect him from the harsh conditions of a freezer. EDIT EDIT EDIT: Then Gmaas ate all the food in sseraj's freezer. He enjoyed the ice cream in the freezer the most. EDIT EDIT EDIT EDIT: Gmaas also ate sseraj's freezer.<br />
<br />
- Gmaas once demanded Epic Games to give him 5,000,000 V-bucks for his 569823rd birthday. EDIT: This is why Gmaas no longer has an Epic Games account. EDIT EDIT: Gmaas created Epic Games, though.<br />
<br />
- Gmaas sightings are not very common. There have only been 30 confirmed sightings of Gmaas in the wild.<br />
<br />
- Gmaas is a sage omniscient cat.<br />
<br />
- Gmaas is looking for suitable places other than sseraj's fridge to live in.<br />
<br />
List of places where Gmaas sightings have happened:<br />
<br />
- The Royal Scoop ice cream store in Bonita Beach Florida<br />
<br />
- Inside the abandoned hospital on Rosevelt Island in New York City, which is also a feral cat sanctuary.<br />
<br />
- MouseFeastForCats/CAT 8 Mouse Apartment 1083<br />
<br />
- Gmaasology 2 (1440)<br />
<br />
- Alligator Swamp A 1072<br />
<br />
- Alligator Swamp B 1073<br />
<br />
- Gmaasology A (1488)<br />
<br />
- Introduction to Gmaasology A (1170)<br />
<br />
- Introduction to Gmaasology B (1529)<br />
<br />
- Welcome to Panda Town Gate 1076<br />
<br />
- Welcome to Gmaas Town Gate 1221<br />
<br />
- Welcome to Gmaas Town Gate 1125<br />
<br />
- 33°01'17.4"N 117°05'40.1"W (Rancho Bernardo Road, San Diego, CA)<br />
<br />
- The other side of the ice in Antarctica<br />
<br />
- Feisty Alligator Swamp 1115<br />
<br />
- Introduction to Gmaasology 1221 (Taught by sseraj)<br />
<br />
- Introduction to Gmaas and Gmaasology 1142<br />
<br />
- Feisty-ish Alligator Swamp 1115 (AGAIN)<br />
<br />
- Advanced Gmaasology and Gmaas Conjuring 1137<br />
<br />
- Intermediate Gmaas and Gmaasology 1207<br />
<br />
- Posting student surveys<br />
<br />
- USF Castle Walls - Elven Tribe 1203<br />
<br />
- The Dark Lord's Hut 1210<br />
<br />
- Gmathamatical Problem Series 1200<br />
<br />
- Intermediate Gmaasology 1138<br />
<br />
- Intermediate Number Theory 1476<br />
<br />
- Introduction to Gmaasology 1204 on July 27, 2016<br />
<br />
- Gmaasology B 1112<br />
<br />
- Intermediate Algebra 1561 7:17 PM 12/11/16<br />
<br />
- Nowhere Else, Tasmania<br />
<br />
- The Gmaathamatics School of Gmaasology<br />
<br />
- Geometry 1694 at 1616 PST military time. There was a boy riding him, and he seemed extremely miffed.<br />
<br />
- Intermediate Gmaasology 1710 9/24/2018<br />
<br />
- Introduction to Gmaasology 1369<br />
<br />
- Introduction to Gmaas and Gmaasology 1177<br />
<br />
Here are some more deleted sighting from an old version of Gmaas:<br />
<br />
- Cat Gathering 1222<br />
<br />
− Introduction to Geometry 1190<br />
<br />
− Cat Meow Meow Purr 1110<br />
<br />
− Introduction to Gmaasology 1447<br />
<br />
− Introduction to Geometry 1535<br />
<br />
− Introduction to Gmaasology A 1392<br />
<br />
- These have all been designated as the most glorious sections of AoPSland now (especially the USF castle walls), but deforestation is so far from threatens the wild areas (i.e. Alligator Swamps A&B).<br />
<br />
- Gmaas has also been sighted in Olympiad Gmaasology 1148.<br />
<br />
- Gmaas has randomly been known to have sent his minions into Gmaasology 2 1163. However, the danger is passed. That class is over.<br />
<br />
- Gmaas once snuck into sseraj's email so he could give a future Gmaasologist an extension in Introduction to Gmaasology 1204. This was 1204 minutes after his sighting on 7/27/16.<br />
<br />
- Gmaas has randomly appeared on top of the USF's Tribal Bases(he seems to prefer the Void Tribe). However, the next day there is normally a puddle in the shape of a cat's underbelly wherever he was sighted. Nobody knows what this does. EDIT: Nobody has yet seen him atop a tribal base yet.<br />
<br />
- Gmaas is often under the disguise of a penguin or cat. Look out for them. EDIT: Gmaas rarely disguises himself as a penguin. EDIT EDIT: He is a cat. EDIT EDIT EDIT: He can be whatever he wants. EDIT EDIT EDIT EDIT: But he likes penguins. (As snacks.)<br />
<br />
- Gmaas lives in the shadows. Is he a dream? Truth? Fiction? Condemnation? Salvation? AoPS site admin? He is all these things and none of them. He is... Gmaas. EDIT: He is an AoPS site admin. EDIT EDIT: He exists. EDIT EDIT EDIT: He is everything.<br />
<br />
- If you make yourself more than just a cat... if you devote yourself to an ideal... and if they can't stop you... then you become something else entirely. A LEGEND. Gmaas now belongs to the ages. EDIT: Gmaas belongs to Gmaas.<br />
<br />
- Is this real life? Is this just fantasy? No, this is Gmaas, the legend. EDIT: This is real life.<br />
<br />
- Aha!! An impostor!!<br />
<br />
http://www.salford.ac.uk/environment-life-sciences/research/applied-archaeology/greater-manchester-archaeological-advisory-service<br />
<br />
(Look at the acronym.)<br />
<br />
GREATER MANCHESTER ARCHAEOLOGICAL ADVISORY SERVICE EDIT: The above fact is slightly irrelevant. EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The previous edit is slightly irrelevant. EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT EDIT: The above fact is slightly irrelevant.<br />
<br />
- Gmaas might have been viewing (with a <math>\frac{99999.\overline{9}}{100000}</math> chance) the Ultimate Survival Forum. He (or is he a she?) is suspected to be transforming the characters into real life. Be prepared to meet your epic swordsman self someday. If you do a sci-fi version of USF, then prepare to meet your Overpowered soldier with amazing weapons one day.EDIT: Gmaas is neither he nor she, Gmaas is above gender. EDIT EDIT: Gmaas is above your door, waiting to pounce on you.<br />
<br />
- Gmaas is love; Gmaas is life. EDIT: Gmaas is a cat. EDIT EDIT: Gmaas can be whatever he wants to be because he is omnipotent. How? The power of Gmaas.<br />
<br />
- The name of Gmaas is so powerful that it radiates Deja Mew.<br />
<br />
- Gmaas is on the list of "Elusive Creatures." If you have questions or want the full list, contact Gmaas himself. That is if you can figure out how to contact him. He doesn't have an email address nor an address to send mail to. In fact nobody knows for sure where he lives or what he looks like. They can only guess and imagine.<br />
<br />
- Gmaas can be summoned using the <math>\tan(90)</math> ritual. Draw a pentagram and write the numerical value of <math>\tan(90)</math> in the middle, and he will be summoned. EDIT: The above fact is incorrect. A user has done this and commented with screenshot proof at the below link, but Gmaas was not summoned. https://artofproblemsolving.com/community/c287916h1291232 EDIT EDIT: The above 'proof' is non-conclusive. The user had only put an approximation.<br />
<br />
- Gmaas's left eye contains the singularity of a black hole if and only if everyone in the world blinks at the same time within a nanosecond. EDIT: That has never happened and thus it does not contain the singularity of a black hole.<br />
<br />
- Lord Grindelwald once tried to make Gmaas into a Horcrux, but Gmaas's fur is protected by the Elder Wand and secure.<br />
<br />
- Despite common belief, Harry Potter did not defeat Lord Voldemort. Gmaas did. EDIT: Harry Potter was actually Gmaas in disguise.<br />
<br />
- The original owner of Gmaas was Gmaas. EDIT: Gmaas will always be the sole owner of Gmaas. [[sseraj]] is just Gmaas's pet.<br />
<br />
- Gmaas was not the fourth Peverell brother, but he ascended into a higher being and now he resides in the body of a cat, as he was before. Is it a cat? We will know. (And the answer is YES.) EDIT: He wasn't the fourth Peverell brother, but he was a cousin of theirs, and he advised Ignotus to give up his cloak.<br />
<br />
- Gmaas may be ordering his cyber hairballs to take the forums, along with microbots. EDIT: His fur is so long that it generates thousands of micro-hairballs per day. EDIT EDIT: However, Gmaas no longer sheds. Most of Gmaas's hairballs are made when Gmaas gets a haircut. EDIT EDIT EDIT: Gmaas hates haircuts.<br />
<br />
- Gmaas rarely frequents the headquarters of the Illuminati. He was their symbol for one yoctosecond, but he soon decided that the job was too low for his power to be wasted on.<br />
<br />
- It has been wondered if Gmaas is the spirit of Obi-Wan Kenobi or Anakin Skywalker in a higher form, due to his strange capabilities and powers. EDIT: Gmaas is neither Anakin Skywalker or Obi-Wan Kenobi as he is trillions of years older. EDIT EDIT: Anakin Skywalker and Obi-Wan Kenobi could have been Gmaas in another form or reincarnated.<br />
<br />
- Gmaas has a habit of sneaking into computers, joining The Network, and exiting out of some other computer. EDIT: Gmaas invented the first computer. He gave it to Charles Babbage for his birthday.<br />
<br />
- Gmaas uses gmewal as his email service. Edit: gnewal went out of business, so Gmaas now doesn't have an email address<br />
<br />
- Gmaas has a bright orange tail with hot pink spirals. Or he had for 15 minutes. That was the 15 minutes after he tried to play Taylor Swift music on his 34,000 year old MP3 player in front of sseraj, who, at the time, was handling a bucket of dangerous, radioactive material.<br />
<br />
- Gmaas is well known behind his stage name, Michael Stevens (also known as Vsauce XD), or his page name, Purrshanks. EDIT: Crookshanks was his brother.<br />
<br />
- Gmaas watchers know that the codes above are NOT years. They are secret codes for the place. But if you've edited that section of the page, you know that. EDIT: The above post is false. The post before the above post has an unknown truth value.<br />
<br />
- Gmaas is a good friend of the TARDIS and the Millennium Falcon.<br />
<br />
- In the Dark Lord's hut, Gmaas was seen watching Doctor Who. Anyone who has seen the Dark Lord's hut knows that both Gmaas and the DL (USF code name of the Dark Lord) love BBC. How Gmaas gave him a TV may be lost to history. And it has been lost.<br />
<br />
- The TV has been noticed to be invincible. Many USF weapons, even volcano rings, have tried (and failed) to destroy it. The last time it was seen was on a Kobold display case outside of a mine. The display case was crushed, and a report showed a spy running off with a non-crushed TV.<br />
<br />
- The reason why Dacammel left the USF is that gmaas entrusted his TV to him, and not wanting to be discovered by LF, Cobra, or Z9, dacammel chose to leave the USF, but is regretting it, as snakes keep spawning from the TV. EDIT: The above fact is somewhat irrelevant. EDIT EDIT. Dacammel gave the TV back to gmaas, and he left the dark side and their cookies alone. EDIT EDIT EDIT: The above fact is relevant. EDIT EDIT EDIT EDIT: Is this the longest chain of edits on AoPS Wiki? EDIT EDIT EDIT EDIT EDIT: Yes. EDIT EDIT EDIT EDIT EDIT EDIT: It is.<br />
<br />
- Gmaas is a Super Duper Uper Cat Time Lord. He has ERROR: NUMBER COULD NOT COMPILE: TOO LONG regenerations and has used<math>3</math>. <cmath>9\cdot12\cdot2\cdot267794=57843504</cmath>.<br />
<br />
- Gmaas highly enjoys destroying squeaky toys until he finds the squeaky part, then destroys the squeaky part. EDIT: In that way Gmaas is similar to a dog.<br />
<br />
- Gmaas loves to eat turnips. At<math> (Error compiling LaTeX. ! Missing </math> inserted.)\frac{13}{32}<math>of the sites he was spotted at, he was seen with a turnip.<br />
<br />
- Gmaas has a secret hidden garden full of turnips under [[sseraj]]'s house.<br />
<br />
- [[sseraj]] is "Gmaas's person."<br />
<br />
- Gmaas has three tails, one for everyday life, one for special occasions, and one that is invisible.<br />
<br />
- Gmaas is a dangerous creature. If you ever meet him, immediately join his army or you will be killed. EDIT: If you ever meet Gmaas, scratch him on the ears. Most cats enjoy that.<br />
<br />
- Gmaas is in alliance with the Cult of Skaro. How did he get an alliance with ruthless creatures that want to kill everything in sight? Nobody knows (except him), not even the leader of the Cult of Skaro.<br />
<br />
- Gmaas lives in Gallifrey and in Gotham City. (He has sleepovers with Batman.)<br />
<br />
- Gmaas is an excellent driver. EDIT: He designed the first driver's license test, although he didn't bother with the permit test. EDIT EDIT: He invented the first car in 1600, but it sunk in the Pacific Ocean. No one has seen it ever since.<br />
<br />
- The native location of Gmaas is the twilight zone.<br />
<br />
- Donald Trump once sang "All Hail the Chief" to Gmaas, 3 days after being sworn in as US President.<br />
<br />
- Gmass likes to talk with Ricard Rusczyk from time to time.<br />
<br />
- Dumbledore never died. Dumbledore was Gmass. Gmass was Death. Gmass is gave the 3 deathly hallows to the 3 brothers. EDIT: Of course Gmass is the entire reason Voldemort is gone now. EDIT EDIT: like we said before, Gmass was Harry Potter. EDIT EDIT: If Gmass hadn't done this, h we all would have been dead cause of Voldemort. EDIT EDIT EDIT: SOOOOO U BETTER BE THANKFULL!!!!!!<br />
<br />
- Gmaas is the reason why the USF has the longest thread on AoPS.<br />
<br />
- [[sseraj]], in 1521 Introduction to Number Theory, posted an image of Gmaas after saying "Who wants to see 5space?" at around 5:16 PM Mountain Time, noting Gmaas was "also 5space". EDIT: He also did it in Introduction to Algebra A once.<br />
<br />
- Gmaas is not retarded. EDIT: Gmaas is the smartest living being on the planet.<br />
<br />
- In Introduction to Number Theory 1521, [[sseraj]] posted an image of a 5space Gmaas fusion. (First sighting) EDIT: It was also confirmed that Gmaas doesn't like ketchup because it was the only food left the photo.<br />
<br />
- In 1447 Introduction to Geometry, [[sseraj]] posted a picture of Gmaas with a Rubik's cube suggesting that Gmaas's has an average solve time of</math> (Error compiling LaTeX. ! Missing <math> inserted.)-GMAAS</math>seconds.<br />
<br />
- Gmaas beat Superman in a fight with ease. EDIT: Gmaas infiltrated Superman's body, then made him kill himself. So, Superman killed Superman.<br />
<br />
- Gmaas is an admin of Roblox. EDIT: He created Roblox.<br />
<br />
- Gmaas traveled around the world, paying so much <math>MONEY</math> just to eat.<br />
<br />
- Gmaas is a confirmed Apex predator and should not be approached, unless in a domestic form.<br />
<br />
Summary of Gmaas's many powers and deeds:<br />
<br />
- When Gmaas subtracts <math>0.\overline{99}</math> from <math>1</math>, the difference is greater than <math>0</math>.<br />
<br />
- Gmaas was shown to have fallen on Wed Aug 23 2017: https://ibb.co/bNrtmk https://ibb.co/jzUDmk<br />
<br />
- Gmaas died on August 24, 2017, but his father, Gmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasmaasrevived him after about 2 mins of being dead.<br />
<br />
- The results of the revival are top secret, and nobody knows what happened.<br />
<br />
- [[sseraj]], in 1496 [[Gmaasology]] 2, said that Gmaas is Santacat.<br />
<br />
- [[sseraj]] likes to post a picture of Gmaas in every class he passes by. EDIT: [[sseraj]] always posts pictures of Gmaas in cat form, but never in polar bear form. EDIT EDIT: Gmaas is rarely in polar bear form.<br />
<br />
- [[sseraj]] posted a picture of Gmaas as an Ewok, suggesting he resides on the moon of Endor. Unfortunately, the moon of Endor is also uninhabitable ever since the wreckage of the Death Star changed the climate there. It is thought Gmaas is now wandering space in search for a home. EDIT: What evidence is there Endor was affected? Other Ewoks still live there. EDIT EDIT: Also, Gmaas doesn't care. He can live there no matter what the climate is. EDIE EDIT EDIT: Gmaas is omnipotent and can live anywhere he wants during his many lives.<br />
<br />
- Gmaas is the lord of the pokemons.<br />
<br />
- Gmaas can communicate with, and sometimes control, any other cats; however, this is very rare, as cats normally have a very strong will.<br />
<br />
- A picture of Gmaas: http://i.imgur.com/PP9xi.png<br />
<br />
- Gmaas met Mike Miller. EDIT: Gmaas ate Mike Miller.<br />
<br />
- Gmaas got mad at [[sseraj]] once, so Gmaas locked [[sseraj]] in [[sseraj]]'s freezer.<br />
<br />
- Then, [[sseraj]] decided to eat all of Gmaas's hidden turnips in the freezer as punishment. EDIT: [[sseraj]] could not eat all of them so, he put the remaining turnips in the fire.<br />
<br />
- Gmaas once ate a pie.<br />
<br />
- A Gmaas bite is 314159265358979323846264 psi.<br />
<br />
- Many people have met Gmaas, although many of these sightings are dubious. EDIT: It is just like alien sightings.<br />
<br />
- Gmaas can talk but normally hates talking.<br />
<br />
- Gmaas likes to eat his own fur. That's why he doesn't have any as of late<br />
<br />
- Gmaas is bigger than an ant. EDIT: so is a regular cat <br />
<br />
- Gmaas once ate the king of the ants. EDIT: Ants do not have kings; they have queens.<br />
<br />
- Gmaas lives somewhere over the rainbow. EDIT: He lives in [[sseraj]]'s house. EDIT EDIT: [[sseraj]] lives somewhere over the rainbow.<br />
<br />
- Gmaas is an obviously omnipotent cat.<br />
<br />
- [[sseraj]] is known to post pictures of Gmaas on various AoPS classrooms. It is not known if these photos have been altered with the editing program called 'Photoshop.'<br />
<br />
- Gmaas<br />
<br />
- [[sseraj]] has posted pictures of Gmaas in Introduction to Algebra before class started with the title "caption contest." Anyone who posted a caption mysteriously vanished in the middle of the night. EDIT: This has happened many times, including in Introduction to Geometric [[Gmaasology]] 1533, among other active classes. The person writing this did participate, and did not disappear. (You could argue Gmaas is typing this through his/her account...)<br />
<br />
- Gmaas once slept in your bed and made it gray.<br />
<br />
- Richard Rusczyk actually Gmaas in disguise. EDIT: That is false. Gmaas is only in one form at a time. EDIT EDIT: This is also false, you are Gmaas and Gmaas owns you.<br />
<br />
- Gmaas is suspected to be a cat in disguise. EDIT: He is a cat in disguise. See the results on the Gmaas poll in the Gmaas forum.<br />
<br />
- Gmaas is a cat but has characteristics of every other animal on Earth. EDIT: Gmaas does not have the characteristic of being able to eat plankton. EDIT EDIT: Yes he does. He just has not decided to reincarnate as a blue whale yet.<br />
<br />
- Pegasus was modeled off Gmaas. EDIT: Pegasus used to be Gmaas's pet, but Pegasus escaped and joined Bellerophon.<br />
<br />
- Gmaas is the ruler of the universe and has been known to be the creator of the species "Gmaasians". EDIT: He is the universe<br />
<br />
- There is a rumor that Gmaas is starting a poll. EDIT: He has. It is on the Gmaas forum, made by his minions.<br />
<br />
- Gmaas is a Persian smoke who ran away, founded GmaasClan, and became a kitty-pet.<br />
<br />
- There is a sport called "Gmaas Hunting" where people try to successfully capture Gmaas in the wild with video/camera/eyes. Strangely, no one has been able to do this, and those that have have mysteriously disappeared into the night. Nobody knows why. Many people have tried Gmaas Hunting, but they never have been successful.<br />
<br />
- Gmaas burped and caused an earthquake.<br />
<br />
- Gmaas once drank from a teacup.<br />
<br />
- GMAAS IS HERE.... PURRRRRRRRRRRRRRRRRRRR EDIT: Gmaas is everywhere. EDIT EDIT: He is behind you.<br />
<br />
- Gmaas made and currently owns the Matrix. EDIT: The above fact is true. Therefore, this is an illusion.<br />
<br />
- Gmaas is the reason Salah will become better than Ronaldo.<br />
<br />
- Who is Gmaas, really? EDIT: Gmaas is a cat.<br />
<br />
− Gmaas is a heavenly being. EDIT: He is immortal.<br />
<br />
- Gmaas is a cat with no fur or tail. In fact he's a human wearing a cat costume. <br />
- Illuminati was a manifestation of Gmaas, but Gmaas decided Illuminati was not great enough for his godly self.<br />
<br />
- [[sseraj]] has met Gmaas, and Gmaas is his best friend. EDIT: [[sseraj]] is Gmaas's great great great great great grandson.<br />
<br />
- Gmaas read Twilight. EDIT: ...and SURVIVED.<br />
<br />
- There is a secret code when put into super smash where Gmaas would be a playable character. Too bad he didn't say it.<br />
<br />
- Gmaas was a tribute to one of the Hunger Games, came out a Victor, and now lives in District 4.<br />
<br />
- Gmaas is the only known creature that will survive the destruction of Earth in 99,999,999 years. EDIT: The Earth will probably die in around 5,000,000,000 years.<br />
<br />
- [[5space]] (side admin) is one of Gmaas's slaves. EDIT: Gmaas owns all AoPS site administrators. EDIT EDIT: He owns Himself.<br />
<br />
Gmaas photos − http://cdn.artofproblemsolving.com/images/f/f/8/ff8efef3a0d2eb51254634e54bec215b948a1bba.jpg<br />
<br />
http://disneycreate.wikia.com/wiki/File:Troll_cat_gif_(1).gif<br />
<br />
He was also sighted here.<br />
<br />
Gmaas in Popular Culture:<br />
<br />
- BREAKING NEWS: A Gmaasologist has found a possible cousin to Gmaas in Raymond Feist's book Silverthorn. They are mountain dwellers, gwali. Not much are known about them either, and when someone asked,"What are gwali?" the customary answer "This is gwali" is returned. Another eminent Gmaasologist is now looking into it.<br />
<br />
- Someone is writing a book about Gmaas.<br />
<br />
- Sighting of Gmaas: https://2017.spaceappschallenge.org/challenges/warning-danger-ahead/and-you-can-help-fight-fires/teams/gmaas/project<br />
<br />
- Oryx the mad god is actually Gmaas wearing a suit of armor. This explains why he is never truly killed.<br />
<br />
- Potential sighting of Gmaas [1]<br />
<br />
- Gmaas has been spotted in some Doctor Who and Phineas and Ferb episodes, such as Aliens of London, Phineas and Ferb Save Summer, Dalek, Rollercoaster, Rose, Boom Town, The Day of The Doctor, Candace Gets Busted, and many more.<br />
<br />
- Gmaas can be found in many places in Plants vs. Zombies Garden Warfare 2 and Bloons TD Battles.<br />
<br />
- Gmaas was an un-credited actor in the Doctor Who story Knock Knock, playing a Dryad. How he shrunk, we will never know.<br />
<br />
- An eminent Gmaasologist is also writing a story about him. He is continuing the book that was started by the professor of Gmaasology at Harvard. When he is done he will post it here.<br />
<br />
- Gmaas is a time traveler from 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 B.C.<br />
<br />
- No one knows if Gmaas is a Mr. Mime in a cat skin, the other way around, or just a downright combination of both. EDIT: Gmaas is an immortal in a cat body.<br />
<br />
- In it, it mentions these four links as things Gmaas is having trouble (specifically technical difficulties). What could it mean? Links:<br />
<br />
https://docs.google.com/document/d/1NZ0XcFYm80sA-fAoxnm7ulMCwdNU75Va_6ZjRHfSHV0<br />
<br />
https://docs.google.com/document/d/1ELN7ORauFFv1dwpU_u-ah_dFJHeuJ3szYxoeC1LlDQg/<br />
<br />
https://docs.google.com/document/d/1oy9Q3F7fygHw-OCWNEVE8d-Uob2dxVACFcGUcLmk3fA<br />
<br />
https://docs.google.com/document/d/1jzb9Q6FmDmrRyXwnik3e0sYw5bTPMo7aBwugmUbA13o<br />
<br />
- Another possible Gmaas sighting?<br />
<br />
-<math> (Error compiling LaTeX. ! Missing </math> inserted.)Another<math>sighting? [3]<br />
<br />
- Yet Another Gmaas sighting? [4]<br />
<br />
- Gmaas has been sighted several times on the Global Announcements forum.<br />
<br />
- Gmaas uses the following transportation: <img> http://cdn.artofproblemsolving.com/images/3/6/8/368da4e615ea3476355ee3388b39f30a48b8dd48.jpg </img><br />
<br />
- When Gmaas was angry, he started world wars 1 & 2. It is only because of Gmaas that we have not had World War 3. EDIT: He was starting to have to get angry in the Cold War, especially around the Cuban Missile Crisis and the Ronald Regan era, but he decided to eat food, which calmed him down.<br />
<br />
- Gmaas is the only cat to have been proved irrational and transcendental, though we suspect all cats fall in the first category.<br />
<br />
- Gmaas belongs to a secret club of transcendental cats. EDIT: That club is located underneath the Eiffel Tower. EDIT EDIT: Gustave Eiffel was Gmaas in disguise and designed the club.<br />
<br />
- Gmaas plays Geometry Dash. His username is D3m0nG4m1n9. EDIT: Gmaas only does this to punish himself. Olympiad Geometry is his least favorite thing to do.<br />
<br />
- Gmaas likes to whiz on the wilzo.<br />
<br />
- Gmaas has been spotted in many AoPS classes, such as AMC 8 Basics. EDIT: Many of the AoPS classes Gmaas has visited can be found in the Gmaas sightings section of this article.<br />
<br />
- Gmaas is cool. EDIT: He was not cool in summer, so he invented air conditioning. EDIT EDIT: He is air conditioning, in fact he is the entire universe.<br />
<br />
- Gmaas hemoon card that does over 9000000 dmg.<br />
<br />
- Gmaas is a skilled swordsman who should not to be mistaken for Puss in Boots. Some say he even trained the mysterious and valiant Meta Knight.<br />
<br />
- Kirby once swallowed Gmaas. Gmaas had to spit him out.<br />
<br />
- Gmaas was the creator of pokemon, and his pokemon card can OHKO anyone in one turn. He is invisible and he will always move first.<br />
<br />
- Gmaas beat Dongmin in The Genius Game Seasons 1, 2, 3, 4, 5, 6, and 7.<br />
<br />
- Gmaas has five letters. Pizza also has five letters. Pizzas are round. Eyes are round. There is an eye in the illuminati symbol. EDIT: Gmaas is a fluffy cat.<br />
<br />
- Gmaas knows both 'table' and 'tabular' in LaTeX, and can do them in his sleep. EDIT: Gmaas invented LaTeX in his sleep.<br />
<br />
- Gmaas does not hate cheddar cheese, but he doesn't love it either.<br />
<br />
- Gmaas is a cat and not a cat. EDIT: He is a cat.<br />
<br />
- Gmaas was born on the sun. EDIT: Not the sun, the suns. He was born on all the suns at once.<br />
<br />
- Gmaas eats tape. EDIT: Gmaas invented tape. EDIT EDIT: Gmaas eats everything. Gmaas eats computers.<br />
<br />
- Gmaas likes Bubble Gum.<br />
<br />
- Thomas Edison did not invent the lightbulb; Gmaas did.<br />
<br />
- Gmaas invented the alphabet. EDIT: Gmaas thought that hieroglyphs were too complicated, so he invented the alphabet.<br />
<br />
- Gmaas eats metal. EDIT: Gmaas once ate so much metal that he turned into a bronze statue.<br />
<br />
- Gmaas is over 9000 years old! EDIT: This is just a DBZ reference, and bears no reality to his true age. EDIT EDIT: Gmaas is trillions of years old.<br />
<br />
- Gmaas is a cat and not a cat. EDIT: He is a cat. EDIT EDIT: This fact has been stated 31,415 times in this article.<br />
<br />
- Gmaas started the Iron Age. EDIT: He thought civilization was getting too advanced. So he sent out the Sea People to destroy civilization.<br />
<br />
- Gmaas made the dinosaurs go extinct. EDIT: That happened when he got angry that a dinosaur stepped on his toe.<br />
<br />
- Gmaas created life.<br />
<br />
- Gmaas created AoPS. EDIT: AoPS was actually born out of a small fraction of Gmaas's abstract reality, and only the sheer amount math can keep it here. (It is also rumored that when he reclaims it, the USF will be deleted, as that is where 83% of the factions of his abstract reality lives, and when people leave USF, more and more escapes.)<br />
<br />
− Gmaas created mathematics.<br />
<br />
- Gmaas does not like Roblox.<br />
<br />
- Gmaas told Steve Jobs to start a company.<br />
<br />
- Gmaas invented Geometry Dash. EDIT: Gmaas hates Olympiad Geometry. [Source: [[sseraj]]]<br />
<br />
- Gmaas got to</math> (Error compiling LaTeX. ! Missing <math> inserted.)infty</math>in Flappy Bird.<br />
<br />
- Gmaas invented Helix Jump.<br />
<br />
- Gmaas can play Happy Birthday on the Violin.<br />
<br />
- Gmaas has mastered Paganini. EDIT: Paganini was Gmaas in disguise. EDIT EDIT: Gmaas was Paganini in one of his 100,000 human lives. He does not have a human life now because he has a cat life.<br />
<br />
- Gmaas discovered Atlantis after one dive underwater.<br />
<br />
- Gmaas made a piano with 89 keys. EDIT: The piano was made out of chocolate. EDIT: He also made a piano bench made out of chocolate.<br />
<br />
- Gmaas can see the future and how to change it.<br />
<br />
- Gmaas has every super power you can imagine. EDIT: Gmaas has more superpowers than you can imagine.<br />
<br />
- Gmaas made a Violin with 9 strings.<br />
<br />
- Gmaas can read 5 books at once. EDIT: It is slightly difficult for Gmaas to do this because he has no fingers. But somehow, Gmaas finds a way. EDIT: He uses his mind to hold open the books.<br />
<br />
- Gmaas eats rubber bands. EDIT: Gmaas once reincarnated as a rubber band. He thought it was the worst period in his life. Eventually he was snapped and reincarnated as a bacterium, which was also boring.<br />
<br />
- Gmaas married Mrs. Norris. EDIT: Mrs. Norris is his second worst enemy. They say keep your enemies close. EDIT: Gmaas eventually divorced Mrs. Norris for her astounding lack of inteligence and short life span.<br />
<br />
- Gmaas can fly faster than anything. EDIT: No one can travel faster than light. EDIT EDIT: Gmaas can.<br />
<br />
- Grumpy cat is his son. EDIT: Grumpy cat is his worst enemy and his son.<br />
<br />
- Gmaas eats paper. EDIT: According to Gmaas, recycled paper tastes the very good. Paper with steak juice on it tastes even better.<br />
<br />
- Gmaas likes lollipops. EDIT: Gmaas was reincarnated as a lollypop. He did not appreciate having spit all over him while he dissolved.<br />
<br />
- Gmaas nibbles on pencils.<br />
<br />
- Gmaas is alive. EDIT: He is both alive and dead. (For reference, see later post.) EDIT EDIT: He can make people alive and dead.<br />
<br />
- Gmaas is Ninja in Fortnite. EDIT: Gmaas possesses Ninja in Fortnite.<br />
<br />
- Gmaas is love; Gmaas is life. EDIT: Scientist do not know how life was formed. Gmaas does.<br />
<br />
- Gmaas taught Richard Rusczyk everything he knows about mathematics. EDIT: Many famous mathematicians have been Gmaas in disguise.<br />
<br />
- Gmaas can control matter by looking at it. EDIT: He once looked at a galaxy while he was angry. Everything in the galaxy exploded.<br />
<br />
- Gmaas created AoPS. EDIT: He created 99% of all websites. 98% of those websites are blank and unreachable, but the ones that are not are interesting.<br />
<br />
- Gmaas is a quantum particle. EDIT: Gmaas is multiple quantum particles. He is a macroscopic collection of them.<br />
<br />
- Gmaas is alive and dead at the same time. EDIT: He is usually alive.<br />
<br />
- Gmaas likes snow. EDIT: Once Gmaas was reincarnated as a polar bear around 1,000,000 years ago. He had the best time of his lives. EDIT EDIT: While he was a polar bear, he ate many fish.<br />
<br />
- GMAAS LIKES THE NEW AOPS UPDATE! EDIT: Are you sure he does? Did you ask him? EDIT EDIT: Yes, I did.<math> (Error compiling LaTeX. ! Missing </math> inserted.)\text{Gmaas is right behind you}<math>EDIT: Gmaas is everywhere. He is in a quantum superposition. He is still in the superposition until someone sees him. The chance of him being behind you is 0.0000000000000000000000000000000000000000000000000000001%. But, you never know. Is he behind you? Is he behind me right now? He is!!! Aaaaaaaaaah... THUMP<br />
<br />
- Gmaas likes his eggs hard boiled.<br />
<br />
- Gmaas doesn't take showers; he only takes bloodbaths.<br />
<br />
- When the bogeyman goes to sleep, he checks his closet for Gmaas.<br />
<br />
- When Gmaas crosses the street, cars have to look both ways.<br />
<br />
- Gmaas has counted to infinity an infinite amount of times.<br />
<br />
- Gmaas pulled the pin in a grenade. 1 billion people died. Then he threw it.<br />
<br />
- Gmaas controls the Illuminati and controls all the world's resources. He also is the ruler of a communist society on Mars.<br />
<br />
- Gmaas has taken the AHSME/AMC 10, AIME, USAJMO, USAMO, and IMO all the years it has come out. It is rumored that for 2018, Gmaas got a 163.5 on the AMC 12A, a 156 on the AMC 12B, and 17 problems right on the AIME I. EDIT: He also got 51 on USAMO.<br />
<br />
- Gmaas has designed most of the AMC tests. EDIT: He didn't design them in 2015 because he was hibernating too long.<br />
<br />
- Gmaas is a koala. EDIT: Gmaas was actually the first koala. He wanted to reincarnate himself into something new, so he created a whole other species. [Source Wikipedia: Koala] EDIT: Gmaas is a Koala when they are not alive, which is 10% of the time. When they are alive, Gmaas is a cat.<br />
<br />
- Time is Gmaas's vacation home. EDIT: Gmaas created time as a science project.<br />
<br />
- Gmaas was once reincarnated as Chuck Norris, but he missed being a cat. Then he became a cat.<br />
<br />
- Gmaas once resided with a certain physicist named Schrödinger, but he left because Schrödinger was too confusing. Granted, nothing is too confusing for Gmaas but Schrödinger also made Gmaas alive and dead, which felt weird.<br />
<br />
- Gmaas once decided to eat a carrot. He decided turnips were better.<br />
<br />
- [[Gmaasology]] used to be called [[Gmaathamatics]]. It was renamed a few years ago. For more information, see the [[Gmaasology]] page. That page needs expanding.<br />
<br />
- \gmaas should be made into a LaTeX command. Its function should be to summon Gmaas.<br />
<br />
-</math> (Error compiling LaTeX. ! Missing <math> inserted.)\gmaas</math><br />
<br />
- Grumpy cat pretends to be a descendent of Gmaas because he is jealous. He is not a descendant of Gmaas.<br />
<br />
- Every IMO Gold Medalist is two of Gmaas, standing on top of each other in a trenchcoat.<br />
<br />
- Gmaas has been everywhere in the world. EDIT: Gmaas has been everywhere in the universe and multiverse.<br />
<br />
- The degree used to be called the Gmaas Arc, but the name was too long for most people, so they switched the name.<br />
<br />
- Gmaas is famous on AoPS. EDIT: Gmaas is AoPS.<br />
<br />
- Gmaas invented every math theorem and in fact invented math.<br />
<br />
- Gmaas made 31.415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983% of memes. EDIT: This is incorrect. This is only an estimate.<br />
<br />
- Gmaas is a Gmaas since Gmaas likes to Gmaas and Gmaas is cool because he is named Gmaas.<br />
<br />
- Gmaas once ate Big Chungus. EDIT: Gmaas also once ate cat food. EDIT EDIT: Gmaas hates cat food. EDIT EDIT EDIT: Gmaas also hates dog food. EDIT EDIT EDIT EDIT: Gmaas does not need to eat, he is an all-conquering god who never/rarely dies. EDIT EDIT EDIT EDIT EDIT: Gmaas is Big Chungus EDIT EDIT EDIT EDIT EDIT EDIT: He was Big Chungus for 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745530506820349625245174939965143142980919065925093722169646151570985838741059788595977297549893016175392846813826868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388439045124413654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767889525213852254995466672782398645659611635488623057745649803559363456817432411251507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858900971490967598526136554978189312978482168299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610213596953623144295248493718711014576540359027993440374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927819119793995206141966342875444064374512371819217999839101591956181467514269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672218256259966150142150306803844773454920260541466592520149744285073251866600213243408819071048633173464965145390579626856100550810665879699816357473638405257145910289706414011097120628043903975951567715770042033786993600723055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816909152801735067127485832228718352093539657251210835791513698820914442100675103346711031412671113699086585163983150197016515116851714376576183515565088490998985998238734552833163550764791853589322618548963213293308985706420467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325974636673058360414281388303203824903758985243744170291327656180937734 seconds. EDIT EDIT EDIT EDIT EDIT EDIT EDIT: This is only an rough estimate<br />
<br />
- Garfield is Gmaas in disguise. EDIT: But Gmaas also created Garfield. He took a Gar and a Field, and added them. Boom. He made Garfield.<br />
<br />
-Gmaas didn't create the world. He didn't create the universe. The didn't create multiverses. He is the world. He is the universe. He is the multiverses<br />
<br />
-Gmaas has a cult with many followers. This is the page for his followers. They pray to him and remember him for his deeds.<br />
<br />
- Garfield ate Gmaas but then Gmaas ate garfield. Then they ate each other. <br />
<br />
- Gmaas has an existential crisis every 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374762387462384701892375039482750198374563145982163097480213759610832479218374918265359801273489123659132706487123987501468509128374981236598123747623874623847018923750394827501983745631459821630974802137596108324792183749182653598012734891236591327064871239875014685091283749812365981237476238746238470189237503948275019837456314598216309748021375961083247921837491826535980127348912365913270648712398750146850912837498123659812374 seconds.<br />
<br />
- Gmaas married and then divorced a picture of himself EDIT: He then destroyed all evidence of this by swallowing it and barfing it out as a hairball<br />
<br />
- Gmaas needed light to read and he turned into a lamp called the sun and created 31.4159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745530506820349625245174939965143142980919065925093722169646151570985838741059788595977297549893016175392846813826868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388439045124413654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767889525213852254995466672782398645659611635488623057745649803559363456817432411251507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858900971490967598526136554978189312978482168299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610213596953623144295248493718711014576540359027993440374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927819119793995206141966342875444064374512371819217999839101591956181467514269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672218256259966150142150306803844773454920260541466592520149744285073251866600213243408819071048633173464965145390579626856100550810665879699816357473638405257145910289706414011097120628043903975951567715770042033786993600723055876317635942187312514712053292819182618612586732157919GMAAS84148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769752456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983% of life. EDIT: Gmaas uses a new type of tetradecimal number system where the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, G, M, A, and S. The number 416877 is Gmaas's favorite integer. (Convert it to this number system)<br />
<br />
-None of this is true. Except for maybe that last one. EDIT: This fact is therefore not true.<br />
<br />
-Gmaas has controlled everyone's mind and made them eat moldy cheeseburgers.<br />
<br />
-You can't PM or email Gmaas. He's a pretty tough guy to talk to. He makes the great hulk look like a mouse. To contact him you have to summon Gmaas' royal guards at his palace. Or you can contact him using a sophisticated and secretive instant messaging system. Which is really just pretending to read minds. <br />
<br />
- remember, EVERY SINGLE thing u do, Gmaas is watching, and when u do bad, or insult him, u will feel regret very soon.Also, if u find cat hair everywhere, but u r not a cat owner,<br />
he is probably visiting your home to see how much math u we doing. So START DOING YOUR MATH KIDS! <br />
<br />
-<aops>X</aops]>sseraj locked Gmaas in his toilet because Gmaas blew the top half of his house.<br />
<br />
-Gmaas once woke up one day, farted, and accidentally created the known universe.<br />
<br />
-Gmaas can destroy every living creature and every imaginary creature, including himself, using only 1% of his power. EDIT: That means he can destroy himself, but he defeats everyone, so this is a paradox. However, this is still possible because of the power of GMAAS.<br />
<br />
-Spelling Gmaas with a lowercase G is disrespectful. Such a insult shall never happen, or the world may be imbalanced to the point of collapsing.<br />
<br />
-Out of all the life that ever existed, 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of it are reincarnations of Gmaas.<br />
<br />
-Gmaas can make so many edits to this holy bible, that it would destroy the known universe.<br />
<br />
(Why is this a thing?) Because we are all worshippers of Gmaas. How dare you suggest such an atrocity?!?!?! You are now hereby banished from the holy bible of Gmaas and shall not make edits ever again! -Decreed by THE ENFORCER<br />
<br />
This article is NOT spam<br />
<br />
Gmaas is actually an AoPS site admin... (And a human) not a cat...<br />
<br />
All hail Gmaas!<br />
<br />
P.S. Gmaas one USAMO 5 times in a row. That's because he invented USAMO. When gmaas took it nobody knew about it and he was the only one who took it. So of course he won. EDIT: How dare you spell Gmaas with a lowercase G?</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=1990_AHSME_Problems/Problem_25&diff=1083391990 AHSME Problems/Problem 252019-08-06T23:36:47Z<p>Vsar0406: /* Solution */</p>
<hr />
<div>== Problem ==<br />
<br />
Nine congruent spheres are packed inside a unit cube in such a way that one of them has its center at the center of the cube and each of the others is tangent to the center sphere and to three faces of the cube. What is the radius of each sphere?<br />
<br />
<math>\text{(A) } 1-\frac{\sqrt{3}}{2}\quad<br />
\text{(B) } \frac{2\sqrt{3}-3}{2}\quad<br />
\text{(C) } \frac{\sqrt{2}}{6}\quad<br />
\text{(D) } \frac{1}{4}\quad<br />
\text{(E) } \frac{\sqrt{3}(2-\sqrt2)}{4}</math><br />
<br />
== Solution ==<br />
Let <math>r</math> be the radius, let <math>C</math> be the center of the cube, and let <math>P</math> be the center of one of the eight outer spheres, noting that <math>PC=2r</math>.<br />
<br />
Back, in the corner of the unit cube, a smaller cube whose inner corner coincides with <math>P</math>. The cube is of dimensions <math>1\times 1\times 1</math> and its space diagonal is of length <math>\sqrt3</math>. Thus the space diagonal of the unit cube is <math>2(r\sqrt3+2r)=\sqrt3</math>. Solving for <math>r</math>, we get <math>\fbox{B}</math><br />
<asy><br />
draw((0,0)--(0,1)--(1,1)--(1,0)--cycle);<br />
for(int i=0;i<4;++i)draw(rotate(i*90,(.5,.5))*circle((0.25,0.25),0.225));<br />
//draw(circle((0.75,0.25),0.225));<br />
draw(circle((0.5,0.5),0.19),dashed);<br />
draw((0,0)--(.5,.5),dotted);<br />
dot((.25,.25));dot((.5,.5));<br />
label("P",(.25,.25),S);label("C",(.5,.5),N);<br />
</asy><br />
<br />
== See also ==<br />
{{AHSME box|year=1990|num-b=24|num-a=26}} <br />
<br />
[[Category: Intermediate Geometry Problems]]<br />
{{MAA Notice}}</div>Vsar0406https://artofproblemsolving.com/wiki/index.php?title=2018_AMC_8_Problems/Problem_23&diff=1080122018 AMC 8 Problems/Problem 232019-07-29T16:04:32Z<p>Vsar0406: /* Solution */</p>
<hr />
<div>From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?<br />
<br />
<asy><br />
size(3cm);<br />
pair A[];<br />
for (int i=0; i<9; ++i) {<br />
A[i] = rotate(22.5+45*i)*(1,0);<br />
}<br />
filldraw(A[0]--A[1]--A[2]--A[3]--A[4]--A[5]--A[6]--A[7]--cycle,gray,black);<br />
for (int i=0; i<8; ++i) { dot(A[i]); }<br />
</asy><br />
<br />
==Solution 1==<br />
<br />
We will use constructive counting to solve this. There are <math>2</math> cases: Either all <math>3</math> points are adjacent, or exactly <math>2</math> points are adjacent.<br />
If all <math>3</math> points are adjacent, then we have <math>8</math> choices. If we have exactly <math>2</math> adjacent points, then we will have <math>8</math> places to put the adjacent points and also <math>4</math> places to put the remaining point, so we have <math>8\cdot4</math> choices. The total amount of choices is <math>{8 \choose 3} = 8\cdot7</math>.<br />
Thus our answer is <math>\frac{8+8\cdot4}{8\cdot7}= \frac{1+4}{7}=\boxed{\textbf{(D) } \frac 57}</math><br />
<br />
==Solution 2 (Complementary)==<br />
<br />
We can decide <math>2</math> adjacent points with <math>8</math> choices. The remaining point will have <math>6</math> choices. However, we have counted the case with <math>3</math> adjacent points twice, so we need to subtract this case once. The case with the <math>3</math> adjacent points has <math>8</math> arrangements, so our answer is <math>\frac{8\cdot6-8}{8\cdot7}=\boxed{\textbf{(D) } \frac 57}</math><br />
<br />
==See Also==<br />
{{AMC8 box|year=2018|num-b=22|num-a=24}}<br />
<br />
{{MAA Notice}}</div>Vsar0406