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List of United States elementary school mathematics competitions
* [https://pimathcontest.com/ Pi Math Contest] is a math competition for elementary, middle, and high school *[[RSM Foundation International Math Contest]] is a two-round Olympiad-style contest for students in grades 3-8. ([https://rsmfound

4 KB (493 words) - 15:26, 29 June 2024
List of United States middle school mathematics competitions
* [https://pimathcontest.org/ Pi Math Contest] is a two-round math competition for elementary and middle school students. *[[RSM Foundation International Math Contest]] is a two-round Olympiad-style contest for students in grades 3-8 ([https://rsmfounda

7 KB (784 words) - 21:07, 29 October 2024
Geometric inequality
The [[Triangle Inequality]] says that the sum of the lengths of any two sides of a non[[degenerate]] triangle is greater than the length of the thi ...area]] <math>A</math> and [[perimeter]] <math>P</math>, then <math>\frac{4\pi A}{P^2} \le 1</math>. This means that given a perimeter <math>P</math> for

7 KB (1,300 words) - 00:11, 28 October 2024
Number theory/Advanced
An elliptic curve is the set of points <math>(x,y)</math> satisfying some two variable third degree equation. Using certain affine transformations it can ...math> or when this line is tangent to the curve, and hence cuts it in only two points.) We define <math>P+Q</math> to be the reflection of <math>R</math>

5 KB (849 words) - 15:14, 18 May 2021
Real number
...any value. Some examples of real numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are <math>\ 3i</math>, ...n the [[algebraic number]]s and [[transcendental number]]s, although these two classes are best understood as subsets of the [[complex number]]s.

3 KB (496 words) - 22:22, 5 January 2022
Circle
...^2</math>. Both formulas involve the mathematical constant [[pi]] (<math>\pi</math>). We shall explore two of the Greek [[mathematician]] [[Archimedes]] demonstrations of the area of

9 KB (1,585 words) - 12:46, 2 September 2024
Ellipse
...ath> to two fixed [[focus|foci]] is a constant. (The equivalence of these two definitions is a non-trivial fact.) ...endicular]] to the axis of the the cone, or (in the second definition) the two foci of the ellipse coincide.

5 KB (892 words) - 20:52, 1 May 2021
Pi
...mber]], as proved by Lindemann in 1882) denoted by the Greek letter <math>\pi </math>. ...^2}=\frac{\pi^2}{6}</math>. Some common [[fraction]]al approximations for pi are <math>\frac{22}{7} \approx 3.14285</math> and <math>\frac{355}{113} \ap

8 KB (1,469 words) - 20:11, 16 September 2022
Logarithm
..., we have <math>\ln (-1)=i\pi</math>. Additionally, <math>\ln (-n)=\ln n+i\pi</math> for positive real <math>n</math>. Two-minute Intro to Logarithms [http://www.youtube.com/watch?v=ey7ttABX9SM]

4 KB (680 words) - 11:54, 16 October 2023
Irrational number
...n [[decimal notation]], never terminates nor repeats. Examples are <math>\pi, \sqrt{2}, e, \sqrt{32134},</math> etc. There are two types of irrational numbers: algebraic and transcendental.

3 KB (368 words) - 18:26, 6 June 2015
Roots of unity
...as a positive real number). This leaves us with <math>e^{ni\theta} = e^{2\pi ik}</math>. ...math> ni\theta = 2\pi ik</math>. Solving this gives <math> \theta=\frac{2\pi k}n </math>. Additionally, we note that for each of <math> k=0,1,2,\ldots,

3 KB (558 words) - 20:36, 11 December 2011
Complex analysis
<cmath> f^{(n)}(z_0)=\frac{n!}{2\pi i} \oint_\Gamma \frac{f(z)\; dz}{(z-z_0)^{n+1}}. </cmath> ...lle's Theorem. If <math>f</math> is an entire function so that there exist two complex numbers <math>a</math> and <math>b</math> such that for every compl

2 KB (271 words) - 21:06, 12 April 2022
LaTeX:Symbols
|<math>\pi</math>||\pi||<math>\varpi</math>||\varpi||<math>\rho</math>||\rho||<math>\varrho</math> | <math>\Xi</math>||\Xi||<math>\Pi</math>||\Pi||<math>\Sigma</math>||\Sigma||<math>\Upsilon</math>||\Upsilon

16 KB (2,315 words) - 20:52, 22 September 2024
2021 JMC 10
...can <math>|\pi - |e - | e - \pi|||</math> be expressed in terms of <math>\pi</math> and <math>e?</math> ...}2\pi-2e\qquad\textbf{(C) }2e\qquad\textbf{(D) }2\pi \qquad\textbf{(E) }2\pi +e</math>

12 KB (1,784 words) - 15:49, 1 April 2021
2006 AMC 12B Problems
...ball game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 po ...they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's s

13 KB (2,058 words) - 11:36, 4 July 2023
2006 AMC 12A Problems
...math> is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is <mat How many sets of two or more consecutive positive integers have a sum of <math>15</math>?

15 KB (2,223 words) - 12:43, 28 December 2020
2004 AMC 12A Problems
...0</math>, or <math>1</math>. How many distinct lines pass through at least two members of <math>S</math>? ...rt3}{2} \qquad \text {(D) } \frac {10\pi}{3} - \sqrt3 \qquad \text {(E) }4\pi - 2\sqrt3</math>

13 KB (1,953 words) - 23:31, 25 January 2023
2003 AMC 12A Problems
The sum of the two 5-digit numbers <math>AMC10</math> and <math>AMC12</math> is <math>123422</ ...}{4}+\frac{1}{24}\pi\qquad \mathrm{(E) \ } \frac{\sqrt{3}}{4}+\frac{1}{12}\pi </math>

13 KB (1,955 words) - 20:06, 19 August 2023
2002 AMC 12A Problems
...\pi \qquad \text{(C)}\ 2\pi \qquad \text{(D)}\ 3\pi \qquad \text{(E)}\ 3.5\pi</math> Two different positive numbers <math>a</math> and <math>b</math> each differ fr

12 KB (1,792 words) - 12:06, 19 February 2020
2001 AMC 12 Problems
The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number a each of the resulting numbers is doubled. What is the sum of the final two

13 KB (1,957 words) - 11:53, 24 January 2024

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