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• Power's of 2 in pascal's triangle
  == Pascal's Triangle == Pascal's Triangle is a triangular array of numbers where each number is the sum of t
  2 KB (341 words) - 16:57, 16 June 2019
• Largange's Interpolation Formula
  44 bytes (4 words) - 13:38, 3 March 2015
• Viete's sums
  #REDIRECT[[Vieta's formulas]]
  29 bytes (3 words) - 00:31, 4 June 2022
• Newton's Inequality
  ...math> in the polynomial <math> \prod_{i=1}^{n}(t+x_i) </math> (see [[Viete's sums]]). We define the ''symmetric average'' <math>d_k </math> to be <math ...have a root between <math>x_i </math> and <math>x_{i+1} </math> by [[Rolle's theorem]] if <math>x_i \neq x_{i+1} </math>, and if <math> x_i = x_{i+1} =
  5 KB (830 words) - 04:05, 28 January 2023
• Maclaurin's Inequality
  ...ymmetric polynomial]]s. For notation and background, we refer to [[Newton's Inequality]]. By the lemma from [[Newton's Inequality]], it suffices to show that for any <math>n </math>,
  992 bytes (146 words) - 16:48, 29 December 2021
• Nesbitt's Inequality
  '''Nesbitt's [[Inequality]]''' is a theorem which, although rarely cited, has many instr If <math> a_1, \ldots a_n </math> are positive and <math> \sum_{i=1}^{n}a_i = s </math>, then
  7 KB (1,224 words) - 16:21, 24 October 2022
• Pascal's Theorem
  '''Pascal's Theorem''' is a result in [[projective geometry]]. It states that if a [[h Since it is a result in the projective plane, it has a dual, [[Brianchon's Theorem]], which states that the diagonals of a hexagon circumscribed about
  4 KB (712 words) - 21:57, 25 April 2020
• Russell's Paradox
  The '''Russell's Paradox''', credited to Bertrand Russell, was one of those which forced the
  580 bytes (100 words) - 17:57, 12 May 2023
• Green's Theorem
  '''Green's Theorem''' is a result in [[real analysis]]. It is continuous [[partial derivative]]s mapping an open set containing
  2 KB (381 words) - 12:12, 30 May 2019
• User:Temperal/The Problem Solver's Resource1
  ...metric proof of the addition case, though other methods, such as de Moivre's Theorem, exist. The following proof is taken from ''the Art of Problem Solv label("$H$",(6,0),S);
  6 KB (1,097 words) - 18:18, 21 January 2016
• User:Temperal/The Problem Solver's Resource2
  This is just a quick review of logarithms and exponents; it's elementary content. ...h>a=\underbrace{b\times b\times b\times \cdots \times b}_{x\text{ }b'\text{s}}</math>, then <math>a=b^x</math>
  2 KB (331 words) - 18:22, 21 January 2016
• User:Temperal/The Problem Solver's Resource4
  ====Cramer's Law==== ====Newton's Sums====
  4 KB (828 words) - 21:45, 27 February 2020
• Talk:Euclid's proof of the infinitude of primes
  364 bytes (52 words) - 11:59, 14 August 2022
• Cramer's Rule
  '''Cramer's Rule''' is a method of solving systems of equations using [[matrix|matrices Cramer's Rule employs the [http://en.wikipedia.org/wiki/Determinant matrix determina
  2 KB (352 words) - 18:22, 11 October 2023
• Ceva's Theorem/Problems
  #REDIRECT[[Ceva's theorem/Problems]]
  36 bytes (4 words) - 16:16, 9 May 2021
• Ceva's theorem/Problems
  530 bytes (82 words) - 16:16, 9 May 2021
• L'Hôpital's Rule
  '''L'Hopital's Rule''' is a theorem dealing with [[limit]]s that is very important to [[calculus]]. ...cdot \epsilon(h)}</math>, which would hence prove our lemma for L'Hospital's rule.
  2 KB (475 words) - 15:04, 24 March 2022
• Zorn's Lemma
  '''Zorn's Lemma''' is a [[set theory | set theoretic]] result which is equivalent to We first prove some intermediate results, viz., Bourbaki's Theorem (also known as the Bourbaki-Witt theorem).
  9 KB (1,669 words) - 19:02, 1 August 2018
• Pascal's Identity
  ...coefficients). It can often be used to simplify complicated [[expression]]s involving binomial coefficients. ...is also known as Pascal's Rule, Pascal's Formula, and occasionally Pascal's Theorem.
  3 KB (496 words) - 15:43, 11 April 2024
• Binet's Formula
  '''Binet's formula''' is an explicit formula used to find the <math>n</math>th term of It's coefficients look like this:
  6 KB (953 words) - 21:37, 30 May 2024

Page text matches

• 1954 AHSME Problems/Problem 46
  label("$E$",(0,0),S);
  3 KB (415 words) - 18:01, 24 May 2020
• 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 (709 words) - 15:00, 1 June 2024
• United States of America Mathematical Olympiad
  ...istered to approximately 500 of the best and brightest students from the U.S. and Canada. Qualification is based on [[AMC 10]], [[AMC 12]], and [[AIME]] ...Olympiad?" in the ''American Mathematical Monthly'' 78 (1971), the [[MAA]]'s National Contest Committee revived an Olympiad Subcommittee, which voted to
  6 KB (869 words) - 12:52, 20 February 2024
• Informatics competitions
  '''Informatics competitions''' test a student's ability to understand, organize, and work with information on computers. * [[St Mary’s University High School Programming Competition]] [http://cs.stmarys.ca/hspc
  7 KB (932 words) - 23:32, 13 June 2024
• Joining an ARML team
  ...nds. Please email Xinke Guo-Xue at xinkeguoxue@gmail.com, or message Xinke's AoPS account "hurdler", if you are interested in trying out for the Alabama ...at the San Diego Math Circle (SDMC), and most of the students on last year's team were regular attendees at SDMC. Also, since the 2007 team contained no
  22 KB (3,533 words) - 20:58, 2 June 2024
• User talk:MCrawford
  When you say that a book is Douglas Adam's only non-fiction work, you need to check around. I think you miss the salmo When leaving messages on other people's user talk pages, it is generally advised to use the "+" button unless you'r
  3 KB (552 words) - 17:10, 28 September 2020
• AoPS Wiki:Spam
  ...ssage boards. The first type is advertising and the second is to raise one's post count or be annoying or unproductive. The first is grounds for an imm
  1 KB (233 words) - 14:36, 17 May 2021
• AoPS Wiki:What AoPSWiki is not
  This is the one most often confused. While it's obvious that AoPSWiki covers a far smaller subject range and is far younger
  2 KB (328 words) - 09:42, 17 October 2022
• AoPS Wiki:Netiquette
  ...cle's discussion page. If the change might cause a lot of controversy, it's advised to discuss changing it on the discussion page ''before'' editing. # Do not edit other people's userpages unless they give you permission to do so.
  4 KB (629 words) - 15:33, 3 January 2024
• Community Service Scholarships
  * Kohl's Kids Who Care Scholarship Program [http://www.kohlscorporation.com/communit
  3 KB (350 words) - 01:18, 19 June 2016
• Mu Alpha Theta
  #10 The set S is {#, !, @, *, $, %}. How many different proper subsets are possible?
  4 KB (632 words) - 17:09, 11 October 2020
• Power Mean Inequality
  The Power Mean Inequality follows from [[Jensen's Inequality]]. As <math>\ln(x)</math> is concave, by [[Jensen's Inequality]], the last inequality is true, proving <math>M(t)\ge M(0)</math
  3 KB (606 words) - 23:59, 1 July 2022
• Wilson's Theorem
  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 [[po
  4 KB (639 words) - 01:53, 2 February 2023
• Trivial Inequality
  For all [[real number]]s <math>x</math>, <math>x^2 \ge 0</math>. ...h> and <math>s</math> are relatively prime positive integers. Find <math>r+s</math>. (Solution [[User:Ddk001#Solution_1.28Probably_official_MAA.2C_lots_
  3 KB (560 words) - 22:51, 13 January 2024
• Heron's Formula
  '''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>
  4 KB (675 words) - 00:05, 22 January 2024
• Polynomial
  ...onnegative]], [[integer|integral]] powers and multiplied by [[coefficient]]s from a predetermined [[set]] (usually the set of integers; [[rational]], [[ ...ly one way (not counting re-arrangements of the terms of the product). It's very easy to find the roots of a polynomial in this form because the roots
  6 KB (1,100 words) - 01:44, 17 January 2024
• Simon's Favorite Factoring Trick
  Simon's Favorite Factoring Trick (SFFT) (made by AoPS user [https://artofproblemsol ...t 1, then divide the coefficient off of the equation.). According to Simon's Favorite Factoring Trick, this equation can be transformed into: <cmath>(x+
  7 KB (1,130 words) - 18:48, 3 June 2024
• Factoring
  Using the formula for the sum of a [[geometric sequence]], it's easy to derive the general formula for difference of powers: == Vieta's/Newton Factorizations ==
  3 KB (532 words) - 22:00, 13 January 2024
• Talk:Simon's Favorite Factoring Trick
  ...est to begin with the brief history of the name, including a link to Simon's post in which he proclaims it his favorite factoring trick.--[[User:MCrawfo ...method is a lot like completing the square, except instead of a square it's a rectangle.
  1 KB (222 words) - 13:50, 12 March 2022
• Proof by contradiction
  ===[[Euclid's proof of the infinitude of primes]]===
  2 KB (374 words) - 14:01, 21 August 2022

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