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Page title matches

• Schonemann's criterion
  See also [[Eisenstein's criterion]].
  1 KB (279 words) - 17:03, 31 October 2023
• Kirchhoff's rules
  Kirchhoff's rules
  406 bytes (67 words) - 20:36, 7 March 2014
• Maine Business & Prof. Women's Club - Rachel E. Lemieux Youth Scholarship
  391 bytes (56 words) - 20:10, 2 December 2015
• KFC Colonel's Scholars Program
  * Plan to pursue a bachelor's degree at a public, in-state college or university
  721 bytes (101 words) - 17:36, 29 June 2022
• The Lowe's Scholarship
  ...for high school seniors who plan to enroll in undergraduate study in the U.S. Students within the U.S., including Lowe's employees and their children, are eligible.
  652 bytes (87 words) - 10:55, 23 July 2010
• Harry S. Truman Scholarship
  * a full-time junior-level student pursuing a bachelor's degree at a four-year institution (see website for a more specific definiti * nominated by the institution's Truman Scholarship Faculty Representative
  2 KB (239 words) - 11:15, 23 July 2010
• Carnot's Thereom
  #REDIRECT [[Carnot's Theorem]]
  30 bytes (3 words) - 20:11, 14 August 2010
• Hensel's Lemma
  55 bytes (9 words) - 17:43, 31 December 2015
• Newton's sums
  27 bytes (3 words) - 17:21, 23 October 2010
• Callebaut's Inequality
  '''Callebaut's Inequality''' states that for <math>1\ge x\ge y\ge 0,</math> <cmath> \sum_{
  1 KB (236 words) - 17:30, 4 December 2010
• ''See also: [[Hölder's Inequality]]'' '''Hölder's Inequality,''' a generalization of the '''Cauchy-Schwarz inequality''', sta
  1 KB (197 words) - 12:12, 29 October 2016
• Hölder's Inequality
  ...n, \dotsc, z_1, z_2, \dotsc, z_n</math> are [[nonnegative]] [[real number]]s and <math>\lambda_a, \lambda_b, \dotsc, \lambda_z</math> are nonnegative re ...||_p^p}, b=\frac{|g(x)|^q}{||g||_q^q},\alpha=1/p,\beta=1/q</math>. [[Young's Inequality]] gives us
  4 KB (762 words) - 00:11, 18 June 2023
• De Moivre's theorem
  #REDIRECT[[De Moivre's Theorem]]
  32 bytes (4 words) - 19:06, 7 February 2023
• ==Proof of l'Hôpital's rule== ...roof of l'Hôpital's rule uses [[Cauchy's mean value theorem]]. l'Hôpital's rule has many variations depending on whether ''c'' and ''L'' are finite or
  4 KB (764 words) - 23:10, 2 January 2012
• Bézout's Identity
  '''Bézout's Identity''' states that if <math>x</math> and <math>y</math> are nonzero [[ ==Generalization/Extension of Bézout's Identity==
  4 KB (768 words) - 16:50, 6 September 2023
• Steiner's Theorem
  '''Steiner's Theorem''' states that in a [[trapezoid]] <math>ABCD</math> with <math>AB\p ...t's not hard to see that <math>\triangle HAB \sim \triangle HCD</math>. It's also not hard to show that <math>\triangle HBE \sim \triangle HDF</math> by
  3 KB (444 words) - 03:02, 23 March 2013
• Euler's Four-Square Identity
  Then Euler's Four-Square Identity simply reads <math>|XY|^2 = |X|^2 |Y|^2</math>; i.e. t
  1 KB (179 words) - 23:24, 5 November 2019
• Dirichlet's Theorem
  805 bytes (138 words) - 12:19, 30 May 2019
• Viviani's theorem
  '''Viviani's Theorem''' states that for an equilateral triangle, the sum of the altitude ...2}=\dfrac{s}{2}(x+y+z)</math>. Therefore, <math>\dfrac{s}{2}(x+y+z)=\dfrac{s}{2}(a)</math>, so <math>x+y+z=a</math>, which means the sum of the altitude
  4 KB (420 words) - 14:13, 4 June 2021
• Euler's inequality
  Euler's Inequality states that <cmath>R \ge 2r</cmath> where R is the circumradius ...he incenter. Then <cmath>d=\sqrt{R(R-2r)}</cmath> From this formula, Euler's Inequality follows as <cmath>d^2=R(R-2r)</cmath> By the [[Trivial Inequalit
  597 bytes (106 words) - 00:44, 25 June 2015

Page text matches

• Elementary symmetric sum
  .../en.wikipedia.org/wiki/Sums_of_powers sums of powers], combined with Vieta's formulas. Elementary symmetric sums show up in [[Vieta's formulas]]. In a monic polynomial of degree <math>n</math>, the coefficient
  2 KB (275 words) - 12:51, 26 July 2023
• Cyclic quadrilateral
  * [[Ptolemy's Theorem]] * [[Brahmagupta's formula]]
  1 KB (162 words) - 20:39, 9 March 2024
• Vieta's Formula
  #REDIRECT[[Vieta's formulas]]
  29 bytes (3 words) - 00:31, 4 June 2022
• Algebra
  ...and usually denoted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]]. ...ebra. [[Group]]s, [[ring]]s, [[field]]s, [[module]]s, and [[vector space]]s are common objects of study in higher algebra.
  3 KB (369 words) - 21:18, 18 June 2021
• Number theory/Advanced
  ...r theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fermat's Last Theorem]].
  5 KB (849 words) - 16:14, 18 May 2021
• Algebra/Intermediate
  ** [[Vieta's Formulas]] ** [[Newton's Sums]]
  2 KB (198 words) - 17:47, 3 November 2021
• Euler's totient function
  '''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 th
  5 KB (898 words) - 19:12, 28 January 2024
• Alabama ARML
  In some years, there are [[Alabama ARML TST]]'s that are written to help decide the team. From 2005-2008, the TST has been
  2 KB (258 words) - 00:50, 28 December 2021
• Contest strategies
  ...ea to stay up all night solving problems or playing video games because it's easy to get drowsy during the test. Getting a good night sleep can help re
  3 KB (538 words) - 13:13, 16 January 2021
• Rearrangement Inequality
  ...tation]] of a [[finite]] [[set]] (in fact, [[multiset]]) of [[real number]]s and <math>B=\{b_1,b_2,\cdots,b_n\}</math> is a permutation of another finit ...ath> and <math>a_k</math> with <math>b_j</math> (unless both a's or both b's are equal, in which case either we can choose another pair of products or n
  5 KB (804 words) - 13:54, 26 January 2023
• Real number
  ...th>, <math>\ 3+2i+2j+k</math>, i.e. [[complex number]]s, and [[quaternion]]s. ...these two classes are best understood as subsets of the [[complex number]]s.
  3 KB (496 words) - 23:22, 5 January 2022
• Divisibility rules
  ...integer]]s are [[divisibility | divisible]] by particular other [[integer]]s. All of these rules apply for [[Base number| base-10]] ''only'' -- other b ...s that are relatively prime to the base (and works GREAT in binary). Here's one that works. 12348 - 28 ==> 12320 ==> 1232 +28 ==> 1260 ==> 126 + 14 ==
  8 KB (1,298 words) - 15:07, 23 May 2024
• Induction
  ...ombinatorics]] are especially susceptible to induction solutions, but that's not to say that there aren't any problems in other areas, such as [[Inequal * Prove Bernoulli's inequality.
  5 KB (768 words) - 20:45, 1 September 2022
• Incenter/excenter lemma
  ...math>L</math> be the midpoint of <math>\overarc{BC}</math> on the triangle's circumcenter. Then, the theorem states that <math>L</math> is the center of
  2 KB (291 words) - 16:31, 18 May 2021
• Triangle
  Triangles are split into six categories; three by their [[angle]]s and three by their side lengths. All the angles of an '''acute''' triangle are [[acute angle]]s.
  4 KB (628 words) - 17:17, 17 May 2018
• Stewart's Theorem
  #REDIRECT[[Stewart's theorem]]
  30 bytes (3 words) - 16:22, 9 May 2021
• Overcounting
  ...other. Suppose we are given an order to count the number of handshakes. It's not a matter of a great deal if there are less than 10 persons. But assume ...s <math>n</math>.So there will be <math>n*(n-1)</math> handshakes. Now let's try our formula for two people. According to the formula we get 2 handshake
  4 KB (635 words) - 12:19, 2 January 2022
• Constructive counting
  ...ulate with <math>4</math> <math>A</math>s and <math>3</math> <math>B</math>s. Using constructive counting is an idea, but there are multiple ways one mi ...xes, so we don't have to account for them after choosing the <math>A</math>s. Thus, there are <math>35</math> different permutations of <math>AAAABBB</m
  12 KB (1,896 words) - 23:55, 27 December 2023
• Jensen's Inequality
  '''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. Taki
  3 KB (623 words) - 13:10, 20 February 2024
• Casework
  ...digit can be <math>9</math> digits, with zero included and the first digit's number removed. Then there are <math>9 + 3 \cdot 81 = 252</math> of these n
  5 KB (709 words) - 10:28, 19 February 2024

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