Create the page "Size" on this wiki! See also the search results found.

• 2016 AMC 10A Problems/Problem 10
  size(6cm);
  2 KB (337 words) - 14:56, 25 June 2023
• 2016 AMC 10A Problems/Problem 11
  size(6cm); size(6cm);
  8 KB (1,016 words) - 00:17, 31 December 2023
• MATHCOUNTS
  ...w states don't need to host chapter competitions due to a small population size.
  10 KB (1,497 words) - 11:42, 10 March 2024
• California MathCounts
  Due to the size and population of the state of [[California]], '''California MathCounts'''
  644 bytes (87 words) - 02:05, 25 March 2015
• Pigeonhole Principle
  Consider the <math>n</math> intervals from <math>[0, 1)</math> of size <math>\frac{1}{n}</math>. We have <math>n+1</math> total <math>b_0, b_1, \l
  11 KB (1,985 words) - 21:03, 5 August 2023
• Geometric mean
  size(150);
  2 KB (282 words) - 22:04, 11 July 2008
• Principle of Inclusion-Exclusion
  ...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. ...ze 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>.
  9 KB (1,703 words) - 07:25, 24 March 2024
• Combination
  ...the number of combinations of size <math>r</math> from an original set of size <math>n</math>
  4 KB (615 words) - 11:43, 21 May 2021
• Fermat's Little Theorem
  ...al proof, this splits the non-main diagonal unit hypercubes into groups of size <math>p</math>, from which it follows that <math>a^p \equiv a \pmod{p}</mat ...a single orbit which we can denote as <math>\mathcal{O}</math> (since the size of the orbit is a factor of <math>p</math>). Hence, if <math>g\ne e</math>
  16 KB (2,658 words) - 16:02, 8 May 2024
• Parabola
  size(300); size(300);
  3 KB (551 words) - 16:22, 13 September 2023
• Geometric inequality
  size(400);
  7 KB (1,296 words) - 14:22, 22 October 2023
• Geometric probability
  ...l outcomes and the number of total outcomes. Instead, we have to find the size of each set. This is where we turn to '''geometric probability'''. We can
  1 KB (175 words) - 23:50, 18 November 2023
• Binomial Theorem
  ...math> is the number of ways to choose <math>m</math> objects from a set of size <math>n</math>, or <math>\binom{n}{m}</math>. Extending this to all possib
  5 KB (935 words) - 13:11, 20 February 2024
• Correspondence
  ...ly used in [[combinatorics]] in order to count the elements of a set whose size is unknown. Bijections are also very important in [[set theory]] when deal
  2 KB (289 words) - 17:17, 13 February 2009
• Bijection
  ...ly used in [[combinatorics]] in order to count the elements of a set whose size is unknown. Bijections are also very important in [[set theory]] when deal
  1,016 bytes (141 words) - 03:39, 29 November 2021
• Combinatorial identity
  We can form a committee of size <math>k+1</math> from a group of <math>n+1</math> people in <math>{{n+1}\ch
  12 KB (1,993 words) - 23:49, 19 April 2024
• Integer
  ...gned <math>32</math>-bit integers). Integers in Python can be of arbitrary size, theoretically limited only by computer memory.
  2 KB (296 words) - 15:04, 5 August 2022
• Ellipse
  size(200); size(200);
  5 KB (892 words) - 21:52, 1 May 2021
• Cardinality
  ...ts, the cardinality of is the number of [[element]]s in that set, i.e. the size of the set. The cardinality of <math>\{3, 4\}</math> is 2, the cardinality For [[infinite]] sets, cardinality also measures (in some sense) the "size" of the set, but an explicit formulation is more complicated: the cardinali
  2 KB (263 words) - 00:54, 17 November 2019
• Vector
  size(150);
  7 KB (1,265 words) - 13:22, 14 July 2021
• Law of Cosines
  size(100);
  6 KB (1,003 words) - 09:11, 7 June 2023
• Rational number
  # Despite this, the set of rational numbers is [[countable]], i.e. the same size as the set of integers.
  1 KB (207 words) - 15:51, 25 August 2022
• Angle bisector
  size(300);
  3 KB (575 words) - 15:27, 19 March 2023
• Area
  ...to the size of the region that a two-[[dimension]]al figure occupies. The size of a region in higher dimensions is referred to as [[volume]].
  6 KB (1,181 words) - 22:37, 22 January 2023
• Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
  <asy>size(250);
  5 KB (912 words) - 20:06, 14 March 2023
• 2002 IMO Shortlist Problems/C5
  ...r </math>, no two of which are disjoint. Prove that there exists a set of size <math> \displaystyle r-1 </math> that meets each set in <math> \displaystyl ...ll stop before <math> \displaystyle |A| = r </math>, for clearly no set of size <math> \displaystyle r </math> can be a subset of every set of <math> \disp
  4 KB (681 words) - 20:10, 19 April 2007
• Rectangle
  size(200);
  782 bytes (108 words) - 13:36, 6 March 2022
• 2006 AIME I Problems
  size(6cm); size(8cm);
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AIME I Problems/Problem 14
  size(200); size(200);
  6 KB (980 words) - 21:45, 31 March 2020
• LaTeX:Symbols
  the parentheses don't come out the right size: ==Multi-Size Symbols==
  16 KB (2,324 words) - 16:50, 19 February 2024
• 2006 AIME I Problems/Problem 11
  ...ze <math>m</math>. Thus, there are 3 times as many towers using blocks of size <math>1, 2, \ldots, m, m + 1</math> as there are towers using only <math>1, ...th>: when <math>m = 1</math>, there are only 2 places to insert a block of size <math>m + 1 = 2</math>, at the beginning or at the end, rather than the 3 p
  3 KB (436 words) - 05:40, 4 November 2022
• 2006 AIME I Problems/Problem 10
  size(150);defaultpen(linewidth(0.7)); size(150);defaultpen(linewidth(0.7));
  4 KB (731 words) - 17:59, 4 January 2022
• 2006 AIME I Problems/Problem 8
  size(8cm); size(8cm);
  5 KB (730 words) - 15:05, 15 January 2024
• 2006 AMC 12B Problems
  size(5cm);
  13 KB (2,058 words) - 12:36, 4 July 2023
• 2006 AMC 12A Problems
  <asy>size(7cm); pointpen = black; pathpen = linewidth(0.7); size(150);
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2004 AMC 12A Problems
  size(150); size(100);
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2002 AMC 12A Problems
  ...an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after size(200);
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2003 AMC 12B Problems
  size(200); size(200);
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2004 AMC 12B Problems
  size(120);
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  ...>8</math>-foot by <math>10</math>-foot floor is tiled with square tiles of size <math>1</math> foot by <math>1</math> foot. Each tile has a pattern consis
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2006 AMC 12B Problems/Problem 10
  If the second size has length x, then the first side has length 3x, and we have the third side
  977 bytes (156 words) - 13:57, 19 January 2021
• 2006 AMC 12B Problems/Problem 21
  size(7cm);
  2 KB (339 words) - 13:15, 12 July 2015
• 2006 AMC 12B Problems/Problem 23
  size(5cm); size(5cm);
  7 KB (1,169 words) - 14:04, 10 June 2022
• 2006 AMC 12B Problems/Problem 24
  size(5cm); size(5cm);
  3 KB (563 words) - 22:45, 24 October 2021
• 2006 AMC 12A Problems/Problem 20
  size(50);
  5 KB (908 words) - 19:23, 22 September 2022
• 2006 AMC 12A Problems/Problem 25
  ...condition. No elements less than <math>s</math> can be put in a subset of size <math>s</math>, therefore the "lowest" element that can go into the subset
  8 KB (1,405 words) - 11:52, 27 September 2022
• 2005 AMC 12A Problems/Problem 25
  ...y solutions as possible, until it becomes intuitive that there are no more size of triangles left. size(200);
  4 KB (498 words) - 00:46, 4 August 2023
• 2005 AMC 12B Problems/Problem 5
  ...-foot by <math>10</math>-foot bathroom floor is tiled with square tiles of size <math>1</math> foot by <math>1</math> foot. Each tile has a pattern consis
  2 KB (223 words) - 14:30, 15 December 2021
• 2005 AMC 12B Problems/Problem 25
  size(30);
  10 KB (1,840 words) - 21:35, 7 September 2023
• 2006 AMC 10A Problems
  size(150); pathpen = linewidth(0.6); defaultpen(fontsize(10)); size(7cm); pathpen = linewidth(0.7);
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2006 AMC 10A Problems/Problem 12
  size(150); pathpen = linewidth(0.6); defaultpen(fontsize(10)); size(150); pathpen = linewidth(0.7); defaultpen(linewidth(0.7)+fontsize(10));
  3 KB (424 words) - 10:14, 17 December 2021
• 2006 AMC 12A Problems/Problem 12
  size(7cm); pathpen = linewidth(0.7);
  2 KB (292 words) - 11:56, 17 December 2021
• 2006 AMC 10A Problems/Problem 16
  size(200); pathpen = linewidth(0.7); pointpen = black; size(200); pathpen = linewidth(0.7); pointpen = black; pointfontpen = fontsize(1
  5 KB (732 words) - 23:19, 19 September 2023
• 2006 AMC 10A Problems/Problem 17
  size(7cm); pathpen = linewidth(0.7); pointpen = black; pointfontpen = fontsize(1 size(7cm); pathpen = linewidth(0.7); pointpen = black; pointfontpen = fontsize(1
  6 KB (1,066 words) - 00:21, 2 February 2023
• 2006 AMC 10A Problems/Problem 24
  size(400);
  2 KB (292 words) - 10:19, 19 December 2021
• Set
  ...[[finite]] set of size <math>n</math> then <math>\mathcal{P}(A)</math> has size <math>2^n</math>. ...y]] of a set <math>A</math>, denoted <math>|A|</math>, is (informally) the size of the set. For a finite set, the cardinality is simply the number of elem
  11 KB (2,021 words) - 00:00, 17 July 2011
• Newman's Tauberian Theorem
  size(200);
  6 KB (1,034 words) - 07:55, 12 August 2019
• 2006 USAMO Problems
  ...ive integers that has sum greater than <math>N </math> but every subset of size <math>k</math> has sum at most <math>N/2</math>.
  3 KB (520 words) - 09:24, 14 May 2021
• 1991 AJHSME Problems
  ...ath>3</math> cm is cut into <math>N</math> smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters
  17 KB (2,246 words) - 13:37, 19 February 2020
• 2005 AIME II Problems/Problem 8
  size(200);
  4 KB (693 words) - 13:03, 28 December 2021
• 2005 AIME II Problems/Problem 12
  size(200); size(200);
  13 KB (2,080 words) - 21:20, 11 December 2022
• 2005 AIME I Problems/Problem 10
  size(170);
  5 KB (852 words) - 21:23, 4 October 2023
• 2005 AIME I Problems/Problem 11
  ...ce it is tangent to two adjacent sides of the square, we will maximize its size when it touches both other sides of the square. This can happen only when
  4 KB (707 words) - 11:11, 16 September 2021
• 2005 AIME I Problems/Problem 13
  defaultpen(fontsize(8)+0.8+heavyblue); size(250);
  5 KB (897 words) - 00:21, 29 July 2022
• 2005 AIME I Problems/Problem 15
  size(300); pointpen=black;pathpen=black+linewidth(0.65); pen s = fontsize(10);
  5 KB (906 words) - 23:15, 6 January 2024
• 2005 AIME II Problems/Problem 15
  size(220); pointpen = black; pen d = linewidth(0.7); pathpen = d; size(220);
  12 KB (2,000 words) - 13:17, 28 December 2020
• 2005 AIME II Problems/Problem 14
  import olympiad; import cse5; import geometry; size(150); import olympiad; import cse5; import geometry; size(300);
  13 KB (2,129 words) - 18:56, 1 January 2024
• 2004 AIME I Problems/Problem 14
  currentprojection = perspective(-2,-50,15); size(200);
  4 KB (729 words) - 01:00, 27 November 2022
• 2004 AIME I Problems/Problem 4
  size(100); size(100);
  3 KB (532 words) - 09:22, 11 July 2023
• 2004 AIME I Problems/Problem 7
  ...,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15]</math>. Denote by <math>S</math> all size 2 subsets of this set. Replace each element of <math>S</math> by the produc
  5 KB (833 words) - 19:43, 1 October 2023
• 2004 AIME II Problems/Problem 7
  size(200);
  9 KB (1,501 words) - 05:34, 30 October 2023
• 2004 AIME II Problems
  size(200);
  9 KB (1,410 words) - 05:05, 20 February 2019
• 1983 AIME Problems
  size(150); size(170);
  7 KB (1,104 words) - 12:53, 6 July 2022
• 1984 AIME Problems
  size(200);
  6 KB (933 words) - 01:15, 19 June 2022
• 2002 AIME I Problems
  size(250);real x=sqrt(3); size(250);
  8 KB (1,374 words) - 21:09, 27 July 2023
• 1983 AIME Problems/Problem 4
  size(150); size(150); defaultpen(linewidth(0.6)+fontsize(11));
  11 KB (1,741 words) - 22:40, 23 November 2023
• 1983 AIME Problems/Problem 11
  size(180); size(180);
  5 KB (865 words) - 21:11, 6 February 2023
• 1983 AIME Problems/Problem 14
  <asy>size(160); defaultpen(linewidth(.8pt)+fontsize(11pt)); dotfactor=3; pair O1=(0,0 size(0,5cm);
  13 KB (2,149 words) - 18:44, 5 February 2024
• 1983 AIME Problems/Problem 15
  <asy>size(100); size(170);
  19 KB (3,221 words) - 01:05, 7 February 2023
• 1984 AIME Problems/Problem 3
  size(200);
  4 KB (726 words) - 13:39, 13 August 2023
• 1985 AIME Problems/Problem 11
  size(200);
  5 KB (932 words) - 17:00, 1 September 2020
• 1985 AIME Problems/Problem 9
  size(200); size(200);
  5 KB (763 words) - 16:20, 28 September 2019
• 1986 AIME Problems/Problem 15
  size(170); size(150);
  11 KB (1,722 words) - 09:49, 13 September 2023
• 1986 AIME Problems/Problem 9
  size(200); size(200);
  11 KB (1,850 words) - 18:07, 11 October 2023
• 1987 AIME Problems/Problem 15
  size(200); size(200);
  5 KB (838 words) - 18:05, 19 February 2022
• 1989 AIME Problems/Problem 15
  size(170); size(170);
  13 KB (2,091 words) - 00:20, 26 October 2023
• 1989 AIME Problems/Problem 12
  defaultpen(fontsize(10)+0.8); size(175);
  2 KB (376 words) - 13:49, 1 August 2022
• 1989 AIME Problems/Problem 10
  size(170); size(170);
  8 KB (1,401 words) - 21:41, 20 January 2024
• 1989 AIME Problems/Problem 8
  size(20cm); size(10cm);
  8 KB (1,146 words) - 04:15, 20 November 2023
• 1989 AIME Problems/Problem 6
  size(300); draw((0,0)--(100,0)--(80,139)--cycle);
  5 KB (864 words) - 19:55, 2 July 2023
• 1990 AIME Problems/Problem 14
  size(280);
  7 KB (1,086 words) - 08:16, 29 July 2023
• 2006 AMC 10B Problems/Problem 6
  size(90); defaultpen(linewidth(0.7));
  1 KB (181 words) - 13:45, 26 January 2022
• 2006 AMC 10B Problems/Problem 8
  defaultpen(linewidth(0.8)); size(100);
  1 KB (176 words) - 13:49, 26 January 2022
• 2006 AMC 10B Problems/Problem 15
  <asy> defaultpen(linewidth(0.7)+fontsize(10)); size(120);
  3 KB (445 words) - 22:01, 20 August 2022
• 1991 AIME Problems/Problem 2
  real r = 0.35; size(220);
  4 KB (595 words) - 12:51, 17 June 2021
• 1992 AIME Problems/Problem 2
  ...ve n people and you want to know how many ways you can make a group of any size you could do this <math>2</math> ways. You could count everyone is binary i
  2 KB (336 words) - 05:18, 4 November 2022
• 2006 AMC 10B Problems/Problem 24
  <asy>size(200);defaultpen(linewidth(0.8));
  4 KB (558 words) - 14:38, 6 April 2024
• 1993 AIME Problems/Problem 13
  size(8cm); defaultpen(linewidth(0.7)); size(8cm); defaultpen(linewidth(0.7));
  8 KB (1,231 words) - 20:06, 26 November 2023
• 1994 AIME Problems/Problem 15
  pathpen = linewidth(1); size(250); pen dots = linetype("2 3") + linewidth(0.7), dashes = linetype("8 6")
  4 KB (717 words) - 22:20, 3 June 2021
• 1994 AIME Problems/Problem 14
  pathpen = linewidth(0.7); size(250);
  2 KB (303 words) - 00:03, 28 December 2017
• 1994 AIME Problems/Problem 7
  <asy> size(150); draw(circle((0,0),sqrt(50)));
  3 KB (442 words) - 19:51, 8 January 2024
• 1994 AIME Problems/Problem 6
  size(200); size(60);
  4 KB (721 words) - 16:14, 8 March 2021
• 1995 AIME Problems/Problem 14
  size(200); pathpen = black + linewidth(0.7); pen d = dashed+linewidth(0.7);
  3 KB (484 words) - 13:11, 14 January 2023
• 1995 AIME Problems/Problem 9
  import graph; size(5cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); p
  7 KB (1,181 words) - 13:47, 3 February 2023
• 1995 AIME Problems/Problem 4
  pointpen = black; pathpen = black + linewidth(0.7); size(150); pointpen = black; pathpen = black + linewidth(0.7); size(150);
  3 KB (605 words) - 11:30, 5 May 2024
• 1996 AIME Problems/Problem 15
  <center><asy>size(180); pathpen = black+linewidth(0.7);
  5 KB (710 words) - 21:04, 14 September 2020
• 1996 AIME Problems/Problem 4
  size(250);defaultpen(0.7+fontsize(9));
  2 KB (257 words) - 17:50, 4 January 2016
• 1997 AIME Problems/Problem 7
  size(200,200);
  4 KB (617 words) - 18:47, 17 July 2022
• 1998 AIME Problems/Problem 13
  It a subset of size 1 has a 9, then its power sum must be <math>9i</math>, and there is only <m
  2 KB (384 words) - 19:02, 20 October 2023
• 1998 AIME Problems/Problem 11
  <span style="font-size:100%">"For non-asymptote version of image, see [[:Image:1998_AIME-11.png]]" size(280); defaultpen(linewidth(0.6)+fontsize(9));
  7 KB (1,084 words) - 11:48, 13 August 2023
• 1998 AIME Problems/Problem 9
  size(180);
  4 KB (624 words) - 18:34, 18 February 2018
• 2000 AIME I Problems/Problem 14
  <center><asy>defaultpen(fontsize(10)); size(200); pen p=fontsize(8); <center><asy>defaultpen(fontsize(8)); size(200); pair A=20*dir(80)+20*dir(60)+20*dir(100), B=(0,0), C=20*dir(0), P=20*
  8 KB (1,275 words) - 03:04, 27 February 2022
• 2000 AIME I Problems/Problem 13
  pointpen = black; pathpen = black+linewidth(0.7); size(250); pointpen = black; pathpen = black+linewidth(0.7); size(250);
  3 KB (571 words) - 00:38, 13 March 2014
• 2000 AIME I Problems/Problem 2
  pointpen = black; pathpen = linewidth(0.7) + black; size(180);
  3 KB (434 words) - 22:43, 16 May 2021
• 2001 AIME I Problems/Problem 7
  ...l triangle <math>ABC</math>. So, <math>DE</math> is <math>43/63</math> the size of <math>BC</math>. Multiplying this ratio by the length of <math>BC</math>
  9 KB (1,540 words) - 08:31, 1 December 2022
• 2001 AIME I Problems/Problem 4
  size(200);
  3 KB (534 words) - 03:22, 23 January 2023
• 2002 AIME I Problems/Problem 15
  size(200);
  7 KB (1,181 words) - 20:32, 8 January 2024
• 2002 AIME I Problems/Problem 14
  ...of the integers in <math>\mathcal{S}</math> be <math>N</math>, and let the size of <math>|\mathcal{S}|</math> be <math>n+1</math>. After any element <math>
  2 KB (267 words) - 19:18, 21 June 2021
• 2002 AIME I Problems/Problem 13
  size(150); pathpen = linewidth(0.7); pointpen = black; pen f = fontsize(8); pair
  6 KB (974 words) - 13:01, 29 September 2023
• 2003 AIME I Problems/Problem 15
  size(400); pointpen = black; pathpen = black+linewidth(0.7);
  8 KB (1,382 words) - 14:23, 29 December 2022
• 2003 AIME I Problems/Problem 12
  pointpen = black; pathpen = black+linewidth(0.7); size(180);
  3 KB (487 words) - 22:14, 24 November 2019
• 2003 AIME I Problems/Problem 10
  pointpen = black; pathpen = black+linewidth(0.7); size(220); pointpen = black; pathpen = black+linewidth(0.7); size(220);
  7 KB (1,058 words) - 01:41, 6 December 2022
• 2003 AIME I Problems/Problem 7
  size(220);
  3 KB (490 words) - 18:13, 13 February 2021
• 2003 AIME I Problems/Problem 6
  size(120); size(120);
  3 KB (477 words) - 18:35, 27 December 2021
• 2003 AIME I Problems/Problem 5
  size(220);
  2 KB (288 words) - 19:58, 4 July 2013
• 2003 AIME II Problems/Problem 14
  size(200); size(200);
  9 KB (1,461 words) - 15:09, 18 August 2023
• 2003 AIME II Problems/Problem 6
  size(8cm);
  5 KB (787 words) - 17:38, 30 July 2022
• 2002 AIME II Problems/Problem 13
  size(10cm); size(10cm);
  6 KB (935 words) - 13:23, 3 September 2021
• 2002 AIME II Problems/Problem 12
  size(150);
  7 KB (1,127 words) - 13:34, 19 June 2022
• 2001 AIME II Problems/Problem 6
  size(150); pointpen = black; pathpen = black+linewidth(0.7); pen d = linetype("4
  4 KB (772 words) - 19:31, 6 December 2023
• 2000 AIME II Problems/Problem 8
  size(200); pathpen = linewidth(0.7);
  4 KB (584 words) - 19:35, 7 December 2019
• 2006 USAMO Problems/Problem 2
  ...ive integers that has sum greater than <math>N </math> but every subset of size <math>k </math> has sum at most <math>N/2 </math>.
  2 KB (398 words) - 09:48, 5 August 2014
• 2006 USAMO Problems/Problem 5
  ...1)</math> and the number <math>2t + 2^{i_0-p} + 1</math> is odd, a jump of size <math>2^{p+1}</math> can be made from <math>2^p(2t + 1) - 2^{i_0}</math> ju
  7 KB (1,280 words) - 17:23, 26 March 2016
• 2006 AMC 12A Problems/Problem 6
  size(175); size(175);
  3 KB (528 words) - 18:29, 7 May 2024
• Radius
  <asy>size(150);
  929 bytes (156 words) - 22:49, 5 January 2023
• 2005 IMO Shortlist Problems/G3
  ...</math> and <math> \displaystyle DY </math>, respectively. Prove that the size of angle <math> \displaystyle KCL </math> does not depend on the choice of
  3 KB (453 words) - 10:53, 24 June 2007
• 2005 AMC 10B Problems
  ...</math>-foot by <math> 10</math>-foot floor is tiled with square tiles of size <math> 1</math> foot by <math> 1</math> foot. Each tile has a pattern consi
  12 KB (1,874 words) - 21:20, 23 December 2020
• Angle bisector theorem
  <asy> size(200); defaultpen(fontsize(12)); real a,b,c,d; pair A=(1,9), B=(-11,0), C=(4
  3 KB (438 words) - 14:20, 4 March 2023
• Mock AIME 2 2006-2007 Problems/Problem 9
  size(200);
  2 KB (358 words) - 23:22, 3 May 2014
• 1970 IMO Problems/Problem 3
  size(10cm,10cm,IgnoreAspect);
  3 KB (577 words) - 16:10, 26 July 2009
• 1995 AHSME Problems/Problem 8
  size(120);
  1 KB (199 words) - 13:58, 5 July 2013
• P versus NP
  ...ministic Turing machine in an amount of time that is [[polynomial]] in the size of the input. More formally, <math>P = \bigcup_{k \ge 0} \text{TIME}(O(n^k)
  6 KB (1,104 words) - 15:11, 25 October 2017
• Congruent (geometry)
  ...over. In plain language, two objects are congruent if they have the same size and shape. size(500);
  10 KB (1,655 words) - 21:43, 24 March 2022
• Committee forming
  ...number of ways to choose a committee of size <math>k</math> from a set of size <math>n</math>. We use <math>{n\choose k}</math> which is called a [[binomi ...us, the problem can be restated as finding the number of committees of any size that can be formed from a group of <math>n</math> people. Each person can
  3 KB (485 words) - 19:49, 16 July 2018
• Power set
  ==Size Comparison== ==Size for Finite Sets==
  4 KB (757 words) - 11:44, 8 March 2018
• Orthocenter
  size(15cm); size(4cm);
  5 KB (829 words) - 13:11, 20 February 2024
• Similarity (geometry)
  ...ects are '''similar''' if they are similar in every aspect except possibly size or orientation. For example, a globe and the surface of the earth are, in
  2 KB (261 words) - 20:42, 25 November 2023
• Chord
  <asy>size(100); <asy>size(120);
  522 bytes (103 words) - 12:16, 18 February 2018
• Stirling number
  ...g the cases that <math>n + 1</math> is in a part of size <math>1</math> or size larger than <math>1</math>.) They can also be calculated using the formula
  2 KB (253 words) - 00:04, 5 December 2020
• 2007 iTest Problems
  size(300);
  33 KB (5,177 words) - 21:05, 4 February 2023
• Asymptote: Basics
  ==Size and Unitsize== The other useful function is <tt>size</tt>, which specifies the exact width and height of the box that your pictu
  5 KB (801 words) - 20:44, 6 May 2024
• Point
  ...is an entity with a location. In [[Euclidean geometry]], points have no [[size]], [[area]], [[length]], or any other characteristics except [[position]].
  3 KB (461 words) - 18:59, 22 April 2008
• 2005 AMC 10A Problems
  size(150);
  14 KB (2,026 words) - 11:45, 12 July 2021
• 2003 AMC 10A Problems
  size(150);
  13 KB (1,900 words) - 22:27, 6 January 2021
• Pick's Theorem
  size(150);
  2 KB (301 words) - 13:08, 20 February 2024
• 2004 AMC 10A Problems
  size(250);defaultpen(linewidth(0.8));
  15 KB (2,092 words) - 20:32, 15 April 2024
• 2003 AMC 12A Problems/Problem 15
  size(150); size(150);
  3 KB (380 words) - 21:53, 19 March 2022
• Sector
  <div style="float:right"><asy>size(150);
  1 KB (178 words) - 21:12, 24 April 2008
• 1987 IMO Problems/Problem 4
  ...>. Thus, <math>g</math> is an invertible function on a finite set of odd size, and hence must have a fixed point, say <math>a \in \mathbb{Z}_{1987}</math
  5 KB (923 words) - 19:51, 21 January 2024
• Vestavia Hills High School Math Tournament
  ...rview Middle of FL and Rickards, GAC, etc. come to compete. Therefore, the size of the competition has grown the past few years. The tests consist of 25 qu
  1 KB (160 words) - 12:31, 27 December 2006
• Georgia Southern Invitational Mathematics Tournament
  ...competition. Individuals and teams are recognized by division and school size. The website contains further information, as well as past exams and resul
  1 KB (154 words) - 09:45, 21 March 2010
• Asymptote: Advanced Configuration
  size(1inch);
  12 KB (1,931 words) - 13:53, 26 January 2020
• Asymptote: Reference
  size(3cm);
  7 KB (1,205 words) - 21:38, 26 March 2024
• Asymptote: Logical Operators and Loops
  size(r*cm); size(r*cm);
  2 KB (324 words) - 16:50, 2 October 2016
• Asymptote: Useful commands and their Output
  size(2cm); size(75);
  6 KB (871 words) - 21:14, 12 June 2023
• Totally ordered set
  ...<math>\{1, 2, 3\}</math> by inclusion (the [[boolean lattice]] on a set of size 3), we don't get a total order because <math>\{1, 2\}</math> and <math>\{3\
  1 KB (174 words) - 12:52, 25 November 2007
• 1960 IMO Problems/Problem 3
  size(8cm);
  3 KB (501 words) - 00:14, 17 May 2015
• 2007 AIME I Problems/Problem 9
  ...the new triangle are <math>\frac{46s}{34s}=\frac{23}{17}</math> times the size of the original. The problem's 16-30-34 triangle sits above the circles.
  11 KB (1,851 words) - 12:31, 21 December 2021
• 2007 AIME I Problems/Problem 12
  defaultpen(fontsize(12)+0.6); size(300);
  10 KB (1,458 words) - 20:50, 3 November 2023
• LaTeX:Downloads
  ##It will ask you your "preferred paper size". North American users will probably want "Letter"; users elsewhere in the
  8 KB (1,318 words) - 01:16, 28 February 2022
• 2007 AIME II Problems/Problem 15
  defaultpen(fontsize(12)+0.8); size(300); defaultpen(fontsize(12)+0.8); size(350);
  11 KB (2,099 words) - 17:51, 4 January 2024
• 1999 ELMO
  |style="font-size:150%;padding:14px 0;margin:0px;text-align:left;white-space:nowrap;color:#00 |style="font-size:130%;margin:0px;text-align:right;white-space:nowrap;color:#000"|
  2 KB (294 words) - 02:36, 13 April 2007
• 2007 USAMO Problems/Problem 3
  ...<math>X</math> in the same class forms <math>k</math> disjoint subsets of size n. ...are in one class. Obviously we can find <math>k</math> disjoint subsets of size n.
  6 KB (1,071 words) - 08:40, 21 October 2020
• 2007 USAMO Problems/Problem 4
  ...of this size that works consists of a center and 4 lines of cells each of size 2006 connected to the center). We next throw out all the [[geometry]] of th ...ubtree if you root from that vertex instead, so you have some subtree with size between <math>\frac{V-1}{D}</math> and <math>\frac V2</math>. Cut the edge
  10 KB (1,878 words) - 14:56, 30 June 2021
• 2007 USAMO Problems/Problem 6
  size(400);
  7 KB (1,274 words) - 15:11, 31 August 2017
• Pascal's Theorem
  size(250);
  4 KB (712 words) - 21:57, 25 April 2020
• 2004 IMO Shortlist Problems/C3
  ...h> \displaystyle A_{n-1} </math>. We then use our procedure for graphs of size <math> \displaystyle n-1 </math> on the subgraph <math> A_1 \cdots A_{n-1}
  4 KB (736 words) - 10:20, 9 June 2007
• LaTeX:Pictures
  We can easily scale the size of the diagram by using the scale optional command. ...LaTeX/Samples/weirdtext.pdf output document] shows text that is doubled in size, rotated 60 degrees, and reflected.
  9 KB (1,454 words) - 16:52, 19 February 2024
• LaTeX:Layout
  ...eft to their defaults. One option that might need modification is the font size, which is 10pt by default but can be increased to 11pt or 12pt. A reference ...portion of the page, enclose that potion in { } and have the relevant font size command occur right at the beginning of the text inside the curly braces. I
  30 KB (5,171 words) - 10:16, 4 April 2021
• LaTeX:Commands
  ...\begin{array}…\end{array} commands, and use \left and \right to properly size the delimiters around the matrix:
  12 KB (1,898 words) - 15:31, 22 February 2024
• Zermelo-Fraenkel Axioms
  This axiom allows us, given a set, to construct other sets of the same size. <br/>
  4 KB (732 words) - 20:49, 13 October 2019
• 2007 AMC 12A Problems/Problem 25
  For subsets of size <math>k</math> there must be <math>2(k - 1)</math> dividers between the bal ...anged in increasing order. This creates a [[bijection]] with the number of size <math>k</math> subsets of the set of the first <math>14-2k</math> positive
  9 KB (1,461 words) - 23:07, 27 January 2024
• 2005 AMC 12A Problems/Problem 15
  import graph; size(7cm);
  14 KB (1,970 words) - 17:02, 18 August 2023
• 2006 AIME II Problems/Problem 12
  size(250); pointpen = black; pathpen = black + linewidth(0.65); pen s = fontsize
  6 KB (1,033 words) - 02:36, 19 March 2022
• 2006 AIME II Problems
  size(50);
  8 KB (1,350 words) - 12:00, 4 December 2022
• 1998 PMWC Problems
  size(2inch);
  11 KB (1,738 words) - 19:25, 10 March 2015
• 1999 PMWC Problems
  import graph; size(3.62cm); import graph; size(4.62cm);
  6 KB (703 words) - 21:21, 21 April 2014
• 2000 PMWC Problems
  ...der and cannot be used any more. Sam wants to make a copy that is the same size as the original document by using the remaining buttons. When he presses a
  11 KB (1,713 words) - 22:47, 13 July 2023
• 2001 PMWC Problems
  size(8cm); size(9cm);
  4 KB (641 words) - 21:24, 21 April 2014
• 2002 PMWC Problems
  size(8cm); size(2cm);
  5 KB (725 words) - 16:07, 23 April 2014
• 2003 PMWC Problems
  size(7cm); size(4cm);
  7 KB (918 words) - 16:15, 22 April 2014
• British Flag Theorem
  size(300);
  3 KB (405 words) - 01:14, 3 December 2023
• 1997 PMWC Problems/Problem I11
  size(4cm);
  944 bytes (154 words) - 12:44, 13 August 2014
• 2004 AMC 10A Problems/Problem 21
  size(85);
  3 KB (476 words) - 03:50, 23 January 2023
• 2004 AMC 12A Problems/Problem 18
  size(100); size(150);
  5 KB (738 words) - 13:11, 27 March 2023
• 2001 IMO Problems/Problem 3
  ...of boys who have solved it. Let this set of problems be A. Clearly, A has size <math>21\times 6</math>.
  2 KB (453 words) - 07:27, 26 November 2020
• 2007 IMO Problems/Problem 3
  ...largest size of a clique contained in one room is the same as the largest size of a clique contained in the other room.
  682 bytes (113 words) - 01:06, 19 November 2023
• Asymptote: Useful functions
  size(8cm,0); <asy>size(200,200);
  4 KB (646 words) - 21:18, 26 March 2024
• Asymptote: CSE5
  size(200); size(200);
  4 KB (607 words) - 15:09, 30 June 2020
• Excircle
  ...sides <math>BX </math> and <math>DY </math>, respectively. Prove that the size of angle <math>KCL </math> does not depend on the choice of <math> \ell </m
  5 KB (843 words) - 03:02, 1 July 2020
• 2001 USAMO Problems/Problem 2
  pathpen = linewidth(0.7); size(300); pen d = linetype("4 4") + linewidth(0.6); pair B=(0,0), C=(10,0), A=7
  11 KB (2,091 words) - 08:35, 16 November 2017
• Magnitude
  ...the number (graphed on the complex plane) to the origin, a measure of the size of a complex number. The magnitude is generally a nonnegative real number.
  2 KB (246 words) - 18:27, 2 March 2023
• Symmetric sum
  ...all <math>\left(\begin{matrix}n\cr r\end{matrix}\right)</math> subsets of size <math>r</math> in <math>\{x_1,\ldots,x_n\}</math>.
  1 KB (255 words) - 12:52, 8 October 2023
• 2004 AMC 12A Problems/Problem 8
  size(150);
  5 KB (692 words) - 21:15, 5 April 2024
• 1992 USAMO Problems/Problem 2
  size(200);
  4 KB (628 words) - 07:41, 19 July 2016
• 2002 AMC 12B Problems/Problem 24
  size(200);
  2 KB (313 words) - 10:23, 4 July 2013
• 2000 AMC 12 Problems/Problem 17
  size(6cm);
  6 KB (979 words) - 12:50, 17 July 2022
• 2000 AMC 12 Problems/Problem 25
  size(8cm); size(8cm);
  7 KB (998 words) - 21:04, 23 December 2023
• 1995 AHSME Problems
  size(100); pathpen = linewidth(0.7); pointpen = black+linewidth(3); ...ning the midpoints of opposite sides. The total number of triangles of any size in the figure is
  17 KB (2,387 words) - 22:44, 26 May 2021
• 1997 PMWC Problems
  import graph; size(5.12cm); import graph; usepackage("amsmath"); size(3.95cm);
  15 KB (2,057 words) - 19:13, 10 March 2015
• 1991 USAMO Problems/Problem 5
  size(220); size(220);
  5 KB (953 words) - 12:18, 4 September 2018
• 1991 USAMO Problems
  size(220);
  3 KB (512 words) - 19:17, 18 July 2016
• 2003 AMC 12B Problems/Problem 22
  size(200);
  4 KB (551 words) - 14:17, 23 June 2022
• 2004 AMC 10A Problems/Problem 19
  size(250);defaultpen(linewidth(0.8));
  2 KB (220 words) - 14:19, 21 April 2021
• 2007 AMC 10A Problems/Problem 24
  size(5cm);
  3 KB (439 words) - 15:39, 3 June 2021
• 2003 AMC 12B Problems/Problem 24
  size(100);
  7 KB (1,183 words) - 11:47, 15 February 2016
• 1998 AHSME Problems/Problem 26
  size(200); size(180);
  3 KB (391 words) - 14:30, 5 July 2013
• 2004 AMC 12B Problems/Problem 24
  size(120);
  2 KB (302 words) - 19:59, 3 July 2013
• 2004 AMC 12B Problems/Problem 19
  size(220); size(220);
  3 KB (520 words) - 19:12, 20 November 2023
• 2002 AMC 10A Problems/Problem 25
  size(250);
  8 KB (1,308 words) - 07:05, 19 December 2022
• 2008 AMC 10A Problems
  size(4cm);
  14 KB (2,138 words) - 15:08, 18 February 2023
• 2008 AMC 12A Problems/Problem 13
  <asy>size(200);
  4 KB (630 words) - 20:32, 4 June 2021
• 2008 AMC 12A Problems/Problem 20
  size(300); size(300);
  6 KB (951 words) - 16:31, 2 August 2019
• List of BBCodes
  ...ze%)]</code></td><td>Changes the size of the text in the specified percent size.</td>
  6 KB (1,152 words) - 18:29, 12 December 2022
• 2004 AMC 12A Problems/Problem 19
  size(400);
  5 KB (785 words) - 00:29, 31 July 2023
• Symmetric group
  ...tion is to be thought of as a [[bijective]] [[function]] from a [[set]] of size <math>n</math> to itself, and the group operation is [[composition]] of fun
  10 KB (1,668 words) - 15:33, 25 May 2008
• 2008 AIME I Problems
  size(200);
  9 KB (1,536 words) - 00:46, 26 August 2023
• 2008 AIME I Problems/Problem 10
  size(300);
  4 KB (629 words) - 22:38, 28 November 2023
• 2008 AIME I Problems/Problem 15
  size(200); size(500);
  6 KB (1,041 words) - 00:54, 1 February 2024
• 2008 AIME I Problems/Problem 14
  size(250); defaultpen(0.70 + fontsize(10)); import olympiad;
  8 KB (1,333 words) - 00:18, 1 February 2024
• 2006 IMO Shortlist Problems/C5
  ...ion our <math>n</math> players into <math>n/2^t</math> different groups of size <math>2^t</math>, it suffices to prove this for <math>n=2^t</math>. ...<math>(n,k)</math>-tournament containing any element of <math>S</math> has size either <math>|S|</math> or <math>2|S|</math>, completing the inductve step
  4 KB (641 words) - 11:09, 30 March 2008
• Mock AIME 1 2007-2008 Problems/Problem 14
  size(220); defaultpen(fontsize(10));
  2 KB (375 words) - 15:23, 25 November 2009
• 2008 AIME II Problems/Problem 5
  size(220); size(220);
  8 KB (1,338 words) - 23:15, 28 November 2023
• 2008 AIME II Problems/Problem 11
  size(200);
  6 KB (1,065 words) - 20:12, 9 August 2022
• 1974 USAMO Problems/Problem 5
  size(400); size(300);
  7 KB (1,221 words) - 18:57, 3 July 2013
• 2005 USAMO Problems/Problem 3
  size(300);
  6 KB (1,117 words) - 01:17, 11 October 2021
• 1998 APMO Problems/Problem 4
  size(200);
  2 KB (345 words) - 18:42, 13 April 2008
• 1997 PMWC Problems/Problem I4
  import graph; size(5.12cm);
  4 KB (356 words) - 07:49, 24 July 2017
• 1997 PMWC Problems/Problem I5
  import graph; usepackage("amsmath"); size(3.95cm);
  2 KB (198 words) - 14:20, 20 April 2014
• Cone
  <center><!-- NOTE: two different versions --><asy> size(120); <asy> size(120);
  7 KB (1,128 words) - 20:12, 27 September 2022
• Mock AIME 1 2007-2008 Problems/Problem 11
  size(150); defaultpen(linewidth(0.8)); import markers; draw(A--E,StickIntervalMarker(1,3,size=6));draw(B--D,StickIntervalMarker(1,3,size=6));
  2 KB (265 words) - 20:02, 29 January 2020
• 2008 AMC 10B Problems/Problem 19
  Let <math>\theta</math> be the size of the smaller angle <math>DAC</math>. We then have <math>\cos\theta = \fra The figure is symmetrical, so the angle <math>CAB</math> has size <math>2\cdot 60^\circ = 120^\circ</math>. Hence the shaded part consists of
  2 KB (373 words) - 13:21, 7 June 2021
• 2008 AMC 10A Problems/Problem 19
  size(220);pathpen=black+linewidth(0.65);pointpen=black;
  2 KB (321 words) - 17:52, 7 November 2021
• 2001 Iran NMO (Round 3) Problems/Problem 5
  size(300);
  3 KB (437 words) - 15:47, 27 April 2008
• 2008 USAMO Problems/Problem 2
  size(280); size(280);
  20 KB (3,565 words) - 11:54, 1 May 2024
• 2008 USAMO Problems/Problem 4
  size(200); defaultpen(linewidth(0.7)+fontsize(10)); size(200); defaultpen(linewidth(0.7)+fontsize(10));
  8 KB (1,318 words) - 12:37, 20 April 2022
• 2008 USAMO Problems/Problem 6
  ...llspace]]. Thus in particular the number of solutions, if non-zero, is the size of the nullspace of <math>A</math>, which is <math>2^{dim(Null(A))}</math> ...gonal of <math>A</math> consists of <math>1</math>s, so this says that the size of the diagonal of this submatrix is even. But this is also the number of <
  13 KB (2,414 words) - 14:37, 11 July 2016
• Fixer
  ...G</math> is <math>S_3</math>, the group of permutations acting on a set of size three, then the fixer of any element of the set is isomorphic to <math>\mat
  2 KB (303 words) - 18:47, 9 September 2008
• 2003 AMC 12A Problems/Problem 17
  size(8cm, 8cm);
  6 KB (1,026 words) - 22:35, 29 March 2023
• Nilpotent group
  ...rjective. Since <math>G</math> and <math>\prod_p P_p</math> have the same size, <math>f</math> is also injective, and hence an [[isomorphism]]. <math>\bl
  9 KB (1,768 words) - 17:55, 5 June 2008

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