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• Pythagorean Theorem
  ...n [[geometry]], and is one of the many tools in a good geometer's arsenal. A very large number of geometry problems can be solved by building right tria In these proofs, we will let <math>ABC </math> be any right triangle with a right angle at <math>{} C </math>.
  5 KB (886 words) - 21:12, 22 January 2024
• 2015 IMO Problems
  We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> ...any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
  4 KB (692 words) - 22:33, 15 February 2021
• Number theory/Advanced
  ...r theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fermat's Last Theorem]]. An elliptic curve is the set of points <math>(x,y)</math> satisfying some two variable third degree equation. Using certain a
  5 KB (849 words) - 16:14, 18 May 2021
• Circle
  A '''circle''' is a geometric figure commonly used in Euclidean [[geometry]]. {{asy image|<asy>unitsize(2cm);draw(unitcircle,blue);</asy>|right|A basic circle.}}
  9 KB (1,555 words) - 20:05, 2 November 2023
• Ellipse
  An '''ellipse''' is a type of [[conic section]]. An ellipse is formed by cutting through a [[cone]] at an [[angle]].
  5 KB (892 words) - 21:52, 1 May 2021
• 2006 AIME I Problems/Problem 8
  ...> is a [[positive integer]], find the number of possible values for <math> K</math>. ...2), F=(-1.65,-1.6), G=(0.45,-1.6), H=(3.75,-1.6), I=(2.1,0), J=(2.1,-3.2), K=(2.1,-1.6);
  5 KB (730 words) - 15:05, 15 January 2024
• 2006 AMC 12A Problems
  {{AMC12 Problems|year=2006|ab=A}} Sandwiches at Joe's Fast Food cost <math>3</math> dollars each and sodas cost <math>2</math> do
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2001 AMC 12 Problems
  The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number and then <math>\text{(A)}\ 2S + 3\qquad \text{(B)}\ 3S + 2\qquad \text{(C)}\ 3S + 6 \qquad\text{(D)
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2004 AMC 12B Problems
  <math>(\mathrm {A}) 3\qquad (\mathrm {B}) 6 \qquad (\mathrm {C}) 9 \qquad (\mathrm {D}) 12 \q In the expression <math>c\cdot a^b-d</math>, the values of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are 0, 1, 2, and
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  A scout troop buys <math>1000</math> candy bars at a price of five for <math>2</math> dollars. They sell all the candy bars at t \mathrm{(A)}\ 100 \qquad
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2005 AIME II Problems/Problem 12
  ...where <math> p,q, </math> and <math> r </math> are [[positive]] [[integer]]s and <math> r </math> is not divisible by the [[square]] of any [[prime]], f ...",G,(-1,1));label("\(O\)",O,(1,-1)); label("\(x\)",E/2+G/2,(0,1));label("\(y\)",G/2+F/2,(0,1)); label("\(450\)",(O+G)/2,(-1,1));
  13 KB (2,080 words) - 21:20, 11 December 2022
• 2005 AIME II Problems/Problem 14
  pair A = origin; pair C = rotate(15,A)*(A+dir(-50));
  13 KB (2,129 words) - 18:56, 1 January 2024
• 2002 AIME I Problems
  ...plate will contain at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right- ...gram shows twenty congruent circles arranged in three rows and enclosed in a rectangle. The circles are tangent to one another and to the sides of the r
  8 KB (1,374 words) - 21:09, 27 July 2023
• 1989 AIME Problems/Problem 10
  ...h>\beta</math>, <math>\gamma</math>, be the angles opposite them. If <math>a^2+b^2=1989c^2</math>, find ...[altitude]] <math>h</math> to <math>c</math>, to get two [[right triangle]]s.
  8 KB (1,401 words) - 21:41, 20 January 2024
• 1995 AIME Problems/Problem 9
  ...,</math> where <math>a</math> and <math>b</math> are integers. Find <math>a+b.</math> ...W); dot((2,0),ds); label("$C$",(2,0),SE); dot((1,0),ds); label("$M$",(1,0),S); dot((1,0.7),ds); label("$D$",(1,0.7),NE);
  7 KB (1,181 words) - 13:47, 3 February 2023
• 2014 USAJMO Problems
  ...frac{10a^2-5a+1}{b^2-5b+10},\frac{10b^2-5b+1}{c^2-5c+10},\frac{10c^2-5c+1}{a^2-5a+10}\right )}\leq abc. </cmath> ...ngle with <math>\angle A=60^\circ</math>, and let <math>O</math> and <math>H</math> denote the circumcenter and orthocenter of <math>\triangle{ABC}</mat
  3 KB (600 words) - 16:42, 5 August 2023
• 2001 AIME I Problems/Problem 6
  .../math> and <math>n</math> are [[relatively prime]] [[positive]] [[integer]]s. Find <math>m + n</math>. ...n the diagram below, the lowest <math>y</math>-coordinate at each of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> corresponds to t
  11 KB (1,729 words) - 20:50, 28 November 2023
• 2000 AIME II Problems/Problem 12
  ...<math>n</math> is not divisible by the square of any prime. Find <math>m+n+k</math>. ...split into <math>9-12-15</math> and <math>5-12-13</math> [[right triangle]]s):
  3 KB (532 words) - 13:14, 22 August 2020
• Dedekind domain
  A '''Dedekind domain''' is a [[integral domain]] <math>R</math> satisfying the following properties: * <math>R</math> is a [[noetherian]] [[ring]].
  9 KB (1,648 words) - 16:36, 14 October 2017
• Congruent (geometry)
  '''Congruency''' is a property of multiple geometric figures. Two [[geometry | geometric]] [[figure]]s are congruent if one of them can be turned and/or flipped and placed exactl
  10 KB (1,655 words) - 21:43, 24 March 2022

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