Difference between revisions of "AoPS Wiki:Sandbox"

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{{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line -->
 
{{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line -->
In the computer world, a '''sandbox''' is a place to test and experiment -- essentially, it's a place to play.
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This is the AoPSWiki Sandbox.  Feel free to experiment here.
 
 
 
Warning: anything you place here is subject to deletion without notice.
 
 
 
[''This was deleted due to its inappropriateness.'']
 
 
 
==Test 1==
 
 
 
<asy>
 
 
 
dot((0,0));
 
 
 
dot((1,3));
 
dot((0,3));
 
dot((0,4));
 
dot((1,4));
 
dot((2,4));
 
dot((3,4));
 
dot((4,4));
 
dot((4,3));
 
dot((4,2));
 
dot((4,1));
 
dot((4,0));
 
dot((5,0));
 
dot((5,1));
 
dot((5,2));
 
dot((5,3));
 
dot((5,4));
 
dot((5,5));
 
dot((4,5));
 
dot((3,5));
 
dot((2,5));
 
dot((1,5));
 
dot((0,5));
 
dot((0,6));
 
dot((1,6));
 
dot((2,6));
 
dot((3,6));
 
dot((4,6));
 
dot((5,6));
 
dot((6,6));
 
dot((6,5));
 
dot((6,4));
 
dot((6,3));
 
dot((6,2));
 
dot((6,1));
 
dot((6,0));
 
dot((7,0));
 
dot((7,1));
 
dot((7,2));
 
dot((7,3));
 
dot((7,4));
 
dot((7,5));
 
dot((7,6));
 
dot((7,7));
 
dot((6,7));
 
dot((5,7));
 
dot((4,7));
 
dot((3,7));
 
dot((2,7));
 
dot((1,7));
 
dot((0,7));
 
draw((0,1)--(1,7),pink);
 
draw((1,7)--(7,6),red);
 
draw((7,6)--(6,0),red);
 
draw((6,0)--(0,1),pink);
 
draw((2,7)--(7,5),blue);
 
draw((0,2)--(2,7),blue);
 
draw((5,0)--(0,2),blue);
 
draw((5,0)--(7,5),red);
 
draw((3,7)--(7,4),green);
 
draw((7,4)--(4,0),black);
 
draw((4,0)--(0,3),green);
 
draw((0,3)--(3,7),pink);
 
draw((4,7)--(7,3),green);
 
draw((7,3)--(3,0),green);
 
draw((3,0)--(0,4),red);
 
draw((0,4)--(4,7),green);
 
draw((5,7)--(7,2),black);
 
draw((7,2)--(2,0),black);
 
draw((2,0)--(0,5),orange);
 
draw((0,5)--(5,7),black);
 
draw((0,6)--(1,0),green);
 
draw((1,0)--(7,1),brown);
 
draw((7,1)--(6,7),brown);
 
draw((0,6)--(6,7),brown);
 
 
 
</asy>
 
Hi there ''yall
 
 
 
==Test 2==
 
<b>Test</b>
 
 
 
<asy>
 
 
 
dot((50,1));
 
dot((2,1));
 
dot((3,1));
 
dot((4,3));
 
dot((5,3));
 
dot((6,3));
 
dot((7,3));
 
dot((1,4));
 
dot((2,4));
 
dot((3,4));
 
dot((4,4));
 
dot((5,4));
 
dot((6,4));
 
dot((7,4));
 
dot((1,5));
 
dot((2,5));
 
dot((3,5));
 
dot((4,5));
 
dot((5,5));
 
dot((6,5));
 
dot((7,5));
 
dot((1,6));
 
dot((2,6));
 
dot((3,6));
 
dot((4,6));
 
dot((5,6));
 
dot((6,6));
 
dot((7,6));
 
dot((1,7));
 
dot((2,7));
 
dot((3,7));
 
dot((4,7));
 
dot((5,7));
 
dot((6,7));
 
dot((7,7));
 
draw((1,1)--(1,3)--(3,3),red);
 
draw((1,4)--(3,4)--(3,2),yellow);
 
draw((4,4)--(4,2)--(2,2),green);
 
draw((4,1)--(2,1)--(2,3),blue);
 
draw((7,1)--(7,3)--(5,3),red);
 
draw((7,4)--(5,4)--(5,2),yellow);
 
draw((4,2)--(6,2),green);
 
draw((4,1)--(6,1)--(6,3),blue);
 
draw((1,7)--(1,5)--(3,5),red);
 
draw((3,4)--(3,6),yellow);
 
draw((4,4)--(4,6)--(2,6),green);
 
draw((4,7)--(2,7)--(2,5),blue);
 
draw((7,7)--(7,5)--(5,5),red);
 
draw((5,4)--(5,6),yellow);
 
draw((4,6)--(6,6),green);
 
draw((4,7)--(6,7)--(6,5),blue);
 
</asy>
 
 
 
This is what epicness looks like.
 
 
 
BUT JEFFCHEN WOULDN'T KNOW
 
 
 
 
 
<asy2>unitsize(33);pair A,B,C,D,I;A=origin; B=1.6*right; C=1.6*dir(60); D=0.8*right;
 
I=incenter(A,B,C); draw(A--B--C--cycle);draw(incircle(A,B,C)); draw(C--D);
 
</asy2>
 
 
 
==Test 3==
 
<asy>
 
dot((0,0));
 
dot((0,4));
 
dot((3,4444));
 
dot((3,0));
 
dot((1.5,2));
 
draw((0,0)--(3,4444),pink);
 
draw((0,4)--(3,0),purple);
 
draw((0,0)--(0,4),green);
 
draw((0,4)--(3,4),blue);
 
draw((3,0)--(3,4),yellow);
 
draw((3,0)--(0,0),red);
 
</asy>
 
 
 
Test 4.0000000000000000000000000000000000000000000000000000000000000000000
 
 
 
 
 
<math>\binom{\binom{3}{2}}{/binom{6}{2}}</math>
 
<math>\sqrt{5}=50</math>
 
HELLO WORLD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
 
 
==Test 5==
 
 
 
n1000 is editing this.
 
yay! (Made better by AoPS)
 
 
 
<asy>
 
pair A,B,C,D,E,F,G,H;
 
 
 
A=(1,0);
 
B=(2,0);
 
C=(3,1);
 
D=(3,2);
 
E=(2,3);
 
F=(1,3);
 
G=(0,2);
 
H=(0,1);
 
 
 
path octagon,square1,square2,star,bow1,bow2;
 
octagon=(A--B--C--D--E--F--G--H--cycle);
 
square1=(A--C--E--G--cycle);
 
square2=(B--D--F--H--cycle);
 
star=(A--D--G--B--E--H--C--F--cycle);
 
bow1=(A--B--F--E--cycle);
 
bow2=(C--D--H--G--cycle);
 
 
 
path[] all;
 
all=(octagon^^square1^^square2^^star^^bow1^^bow2);
 
 
 
draw(all);
 
 
 
fill(octagon,pink);
 
fill((bow1)^^(bow2),purple);
 
fill(all,evenodd+blue);
 
 
 
</asy>
 
 
 
 
 
Who loves me?
 
only <math>x^2</math>
 
 
 
==Test 6==
 
 
 
NeoMathematicalKid was here. And he broke the line of asy diagrams.
 
 
 
<math>\begin{align*}\sum^4_{k=1}\left(\sum^k_{j=1}kj\right)&=\sum^4_{k=1}\left(k\sum^k_{j=1}j\right)\\
 
&=\sum^4_{k=1}\left(k(1+2+\cdots +k)\right)\\
 
&=\sum^4_{k=1}(k+2k+\cdots +k^2)\\
 
&=(1)+(2+4)+(3+6+9)+(4+8+12+16)\\
 
&=1+6+18+40\\
 
&=\boxed{65}
 
\end{align*}</math>
 
notice how the square root signs are becoming progressively less slanted...
 
What is <math>\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{e^{1\pi\pi\sqrtpi}}}}}}+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{20}}}}}}</math>?!?! I got carried away.
 
 
 
==Test 7==
 
<math>\text{Use a calculator:}</math>
 
 
 
<math>\sum^{9}_{k=0} \pi-42</math>!
 
 
 
silentazn's trillion dollar question
 
 
 
bobthesmartypants's answer: There is not enough space in the observable universe to write this number down, so there s no valid answer.
 
my answer: There's not enough matter in the observable universe to store this number in memory, so you don't know the valid answer.
 

Latest revision as of 16:50, 29 October 2024

Welcome to the sandbox, a location to test your newfound wiki-editing abilities.

Please note that all contributions here may be deleted periodically and without warning.

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