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• 1954 AHSME Problems/Problem 46
  pair A=(-3*sqrt(3)/32,9/32), B=(3*sqrt(3)/32, 9/32), C=(0,9/16); pair O=(0,3/8);
  3 KB (415 words) - 18:01, 24 May 2020
• Geometric mean
  ...following situation: if <math>AB</math> is a [[chord]] of [[circle]] <math>O</math> with [[midpoint]] <math>M</math> and <math>M</math> divides the [[di pair A=(3,4),B=(3,-4),M=(3,0);
  2 KB (282 words) - 22:04, 11 July 2008
• Fermat's Little Theorem
  real r = 0.3, row1 = 3.5, row2 = 0, row3 = -3.5; for(int i = 0; i < colors.length; ++i){
  16 KB (2,658 words) - 16:02, 8 May 2024
• Number theory/Advanced
  ...vertically upward as the point at infinity. We denote it by <math>\mathcal{O}</math>. ...>-axis. We may thus summarize the group law by saying <math>P+Q+R=\mathcal{O}</math> if and only if <math>P,Q</math> and <math>R</math> lie on a line.
  5 KB (849 words) - 16:14, 18 May 2021
• 1988 AJHSME Problems/Problem 5
  draw((1.5,0)..(0,1.5)..(-1.5,0)); draw((2.5,0)..(0,2.5)..(-2.5,0)--cycle);
  1 KB (160 words) - 16:53, 17 December 2020
• Law of Sines
  pair A=(-1,5), B=(-4,-1), C=(4,-1), D, O; O = circumcenter(A,B,C);
  4 KB (658 words) - 16:19, 28 April 2024
• Homothety
  ...ABCD</math> and <math>A'B'C'D'</math> are homothetic with respect to <math>O</math>. dot((0,0));
  3 KB (532 words) - 01:11, 11 January 2021
• 2000 AMC 12 Problems/Problem 1
  ...2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? ...clear that this is true, and in this situation, the value of <math>I + M + O</math> would be <math>18</math>. Now, we use this process on <math>2001</ma
  2 KB (276 words) - 05:25, 9 December 2023
• Trigonometry
  ...'''C'''osine = '''A'''djacent / '''H'''ypotenuse, and '''T'''angent = '''O'''pposite / '''A'''djacent ..., the circle with radius one centered at the origin. Starting at <math>(1, 0)</math>, walk a distance <math>\theta</math> counterclockwise around the un
  8 KB (1,217 words) - 20:15, 7 September 2023
• Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
  ...1^{n_4}+\cdots+x_a^{n_4}}{a}}</cmath> where <math>n_1>1,~~0<n_2<1,~~-1<n_3<0,~~n_4<-1</math>, and <math>n</math> is the root mean power. ...m of <math>1^{\infty}</math>. Then, we can say that the limit as x goes to 0, the result goes to the geometric mean of the numbers.
  5 KB (912 words) - 20:06, 14 March 2023
• Riemann Hypothesis
  ...al equation]] for the zeta function, it is easy to see that <math>\zeta(s)=0</math> when <math>s=-2,-4,-6,\ldots</math>. These are called the trivial z ...nt statement of the Riemann hypothesis is that <math>\pi(x)=\mathrm{Li}(x)+O(x^{1/2}\ln(x))</math>.
  2 KB (425 words) - 12:01, 20 October 2016
• Algebraic geometry
  ...ime ideal]] of <math>R</math>. Then <math>V(I)=\{p\in\mathbb{A}^n\mid f(p)=0\mathrm{\ for\ all\ } f\in I\}</math> is called an '''affine algebraic varie ...topological space isomorphic to some <math>(\operatorname{Spec }A,\mathcal{O}_{\operatorname{Spec}A})</math>.
  2 KB (361 words) - 01:59, 24 January 2020
• 2006 AIME I Problems/Problem 14
  ...pointpen=black;pathpen=black+linewidth(0.65);pen ddash = dashed+linewidth(0.65); triple O=(0,0,0),T=(0,0,5),C=(0,3,0),A=(-3*3^.5/2,-3/2,0),B=(3*3^.5/2,-3/2,0);
  6 KB (980 words) - 21:45, 31 March 2020
• 2006 AIME I Problems/Problem 13
  ...<math>S</math> that are divisible by <math>2^n</math>, <math>2^1 - 2^0 = 2^0</math> elements of <math>S</math> that are divisible by <math>2^{n-1}</math ...ath>n<1000</math>, we have five choices for <math>k</math>, namely <math>k=0,2,4,6,8</math>.
  10 KB (1,702 words) - 00:45, 16 November 2023
• LaTeX:Symbols
  |<math>{\oe}</math>||{\oe}||<math>{\ae}</math>||{\ae}||<math>{\o}</math>||{\o} ...<math>{\AE}</math>||{\AE}||<math>{\AA}</math>||{\AA}||<math>{\O}</math>||{\O}
  16 KB (2,324 words) - 16:50, 19 February 2024
• 2006 AMC 12B Problems
  \text {(A) } - 2006 \qquad \text {(B) } - 1 \qquad \text {(C) } 0 \qquad \text {(D) } 1 \qquad \text {(E) } 2006 \text {(A) } 0 \qquad \text {(B) } \frac 34 \qquad \text {(C) } 1 \qquad \text {(D) } 2 \q
  13 KB (2,058 words) - 12:36, 4 July 2023
• 2005 AMC 12A Problems
  pair D=(0,0), C=(1,0), B=(1,1), A=(0,1); pair F=intersectionpoints(Circle(D,2/sqrt(5)),Circle(A,1))[0];
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2000 AMC 12 Problems
  ...2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad
  13 KB (1,948 words) - 12:26, 1 April 2022
• 2003 AMC 12B Problems
  \text {(A) } 0.75 \qquad \text {(B) } 0.8 \qquad \text {(C) } 1.35 \qquad \text {(D) } 1.5 \qquad \text {(E) } 3 \text {(A) } 0 \qquad \text {(B) } 13 \qquad \text {(C) } 37 \qquad \text {(D) } 64 \qquad
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2004 AMC 12B Problems
  ...of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum p defaultpen(0.8);
  13 KB (2,049 words) - 13:03, 19 February 2020

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