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- In [[number theory]], '''Wilson's Theorem''' states that if [[integer ]]<math>p > 1</math> , then <math>(p-1) ...e. Consider the [[field]] of integers modulo <math>p</math>. By [[Fermat's Little Theorem]], every nonzero element of this field is a root of the [[po4 KB (639 words) - 00:53, 2 February 2023
- '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula | formula]] for finding the [[area]] o <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math>5 KB (783 words) - 17:58, 1 January 2025
- *Two different [[prime number]]s between <math>4</math> and <math>18</math> are chosen. When their sum is su ...+2n+108</math> can be factored into <cmath>(k+2)(n+54)</cmath> using Simon's Favorite Factoring Trick. Now, look at n. Then, since the problem tells us4 KB (682 words) - 12:13, 8 December 2024
- #REDIRECT[[Vieta's formulas]]29 bytes (3 words) - 13:40, 5 November 2021
- Mill's Constant is defined as the smallest real number <math>\theta</math> such th ...smallest element in that set. If the [[Riemann Hypothesis]] is true, Mill's constant is approximately <math>1.3063778838630806904686144926...</math> an794 bytes (105 words) - 00:59, 15 January 2022
- #REDIRECT[[Ceva's theorem]]27 bytes (3 words) - 15:06, 9 May 2021
- '''Fermat's Little Theorem''' is highly useful in [[number theory]] for simplifying the A frequently used corollary of Fermat's Little Theorem is <math>a^p \equiv a \pmod {p}</math>. As you can see, it i16 KB (2,660 words) - 22:42, 28 August 2024
- '''Chebyshev's inequality''', named after [[Pafnuty Chebyshev]], states that if ...nce of the [[Rearrangement inequality]], which gives us that the sum <math>S=a_1b_{i_1}+a_2b_{i_2}+...+a_nb_{i_n} </math> is maximal when <math>i_k=k</m1 KB (214 words) - 19:32, 13 March 2022
- '''Euler's Totient Theorem''' is a theorem closely related to his [[totient function]] Let <math>\phi(n)</math> be [[Euler's totient function]]. If <math>n</math> is a positive integer, <math>\phi{(n)4 KB (569 words) - 21:34, 30 December 2024
- .../math>, <math>c</math>, <math>d</math> are the four side lengths and <math>s = \frac{a+b+c+d}{2}</math>. <cmath>16[ABCD]^2=16(s-a)(s-b)(s-c)(s-d)</cmath>3 KB (543 words) - 18:35, 29 October 2024
- #REDIRECT[[Ptolemy's theorem]]30 bytes (3 words) - 16:37, 9 May 2021
- ...[equality condition | equality case]] of [[Ptolemy's Inequality]]. Ptolemy's theorem frequently shows up as an intermediate step in problems involving i ...ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>:7 KB (1,198 words) - 08:36, 8 December 2024
- #REDIRECT[[Vieta's formulas]]29 bytes (3 words) - 23:31, 3 June 2022
- '''Euler's totient function''' <math>\phi(n)</math> applied to a [[positive integer]] ...p_m^{e_m} </math> where the <math>p_i </math> are distinct [[prime number]]s. Now, we can use a [[PIE]] argument to count the number of numbers less th5 KB (903 words) - 14:49, 27 July 2024
- #REDIRECT[[Stewart's theorem]]30 bytes (3 words) - 15:22, 9 May 2021
- '''Jensen's Inequality''' is an inequality discovered by Danish mathematician Johan Jen One of the simplest examples of Jensen's inequality is the [[quadratic mean]] - [[arithmetic mean]] inequality. Taki3 KB (628 words) - 05:29, 28 November 2024
- '''Ptolemy's Inequality''' is a famous inequality attributed to the Greek mathematician *[[Ptolemy's Theorem]]3 KB (602 words) - 08:01, 7 June 2023
- '''Muirhead's Inequality''' states that if a sequence <math>p</math> [[Majorization|major ...ath> majorizes <math>(4,2)</math> (as <math>5>4, 5+1=4+2</math>), Muirhead's inequality states that for any positive <math>x,y</math>,8 KB (1,346 words) - 11:53, 8 October 2023
- ...hat order) and [[diagonal]]s of length <math>p, q</math>. '''Bretschneider's formula''' states that the [[area]] [[Lagrange's Identity]] states that <math>|\vec{a}|^2|\vec{b}|^2-(\vec{a}\cdot\vec{b})^23 KB (566 words) - 02:51, 12 February 2021
- ...hur's Inequality''' is an [[inequality]] that holds for [[positive number]]s. It is named for Issai Schur. Schur's inequality states that for all non-negative <math>a,b,c \in \mathbb{R}</mat2 KB (398 words) - 15:57, 29 December 2021
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- ...theorems in [[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 label("$G$", G, S);5 KB (885 words) - 22:03, 5 October 2024
- ...tangent to both axes and to the second and third circles. What is <math>r/s</math>? label("$s$",(-1.5,4));2 KB (307 words) - 23:58, 17 November 2024
- ...ers and Emilio adds his numbers. How much larger is Star's sum than Emilio's?967 bytes (143 words) - 02:18, 27 June 2023
- ...lish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays <math>40</math> coins in toll to Rabbit after ea1 KB (169 words) - 13:59, 8 August 2021
- If you continue from solution one's conclusion that <cmath>\frac{N(N+1)}{2}=2016</cmath>, the equation can be s2 KB (395 words) - 22:29, 3 December 2024
- The second line's equation can be found in a similar fashion. Its slope is <math>m = \frac{0-8 KB (1,016 words) - 23:17, 30 December 2023
- * [[Math Kangaroo]] may be the world's largest [[mathematics competition]]. [https://youtu.be/Z_lj8xIFRfw?si=oCLT5 KB (512 words) - 08:27, 17 November 2024
- ...tions in the United States. These exams lead up to the selection of the U.S. team for the [[International Mathematical Olympiad]]. ([http://www.maa.org * [https://simiode.org/scudem SIMIODE SCUDEM] -- SIMIODE's (Systemic Initiative for Modeling Investigations and Opportunities using Di6 KB (625 words) - 15:24, 14 December 2024
- There's also some exams with the part of mathematics being as hard as an olympiad,4 KB (414 words) - 16:14, 7 January 2025
- Alabama's math competition community is fairly large and active and there are a numbe ...Math Tournament]]-- Grades 7-12. The VHHS tournament is one of the nation's largest local math tournaments, drawing around 1700 students annually.3 KB (411 words) - 20:32, 8 December 2014
- * [[Women's Technology Program]] at [[MIT]], [http://wtp.mit.edu/ Website]14 KB (1,894 words) - 09:54, 3 January 2025
- ...shift, six days a week. The lead instructors are mathematicians with Ph.D.s and the apprentice instructors are graduate or undergraduate math students. Here's what the {MathILy, MathILy-Er} application process looks like:5 KB (706 words) - 22:49, 29 January 2024
- * [[Moody's Mega Math Challenge]] [http://m3challenge.siam.org/ website]3 KB (408 words) - 01:16, 11 December 2024
- * National Science Foundation's Robert Noyce Scholarship. <dollar/>10,000 for undergraduate or graduate stu * American Meteorological Society's undergraduate scholarships and graduate fellowships for students in STEM ma7 KB (851 words) - 09:54, 29 January 2022
- * Current high school senior enrolled in a U.S. high school * U.S Citizen or permanent resident894 bytes (123 words) - 14:48, 13 June 2022
- * [[Mathematical Kangaroo]] is perhaps the world's largest [[mathematics competition]]. * [[Mathematical Kangaroo]] is perhaps the world's largest [[mathematics competition]].4 KB (417 words) - 13:10, 29 December 2024
- An individual's score is their total number of correct sprint round answers plus 2 times th ...ided by 4 plus 2 points for every correct team round answer, making a team's maximum possible score 66 points. Therefore, it is possible to win with a r10 KB (1,504 words) - 13:10, 1 December 2024
- *[https://sites.google.com/view/tka-math-tournament/home The King's Academy Math Tournament (TKAMT)]4 KB (552 words) - 15:08, 31 December 2024
- * [[St. Mary's Academy Math Team Challenge]] -- Contests for middle school students. [http2 KB (224 words) - 23:51, 28 January 2019
- *[[Soli Deo Gloria Fall Tournament, aka Billy's Math Meet]] [[User:Solafidefarms/MathMeet]]4 KB (503 words) - 06:50, 17 September 2024
