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• Law of Cosines
  The '''Law of Cosines''' is a theorem which relates the side-[[length]]s and [[angle]]s of a [[triangle In the case that one of the angles has measure <math>90^\circ</math> (is a [[right angle]]), the corresponding statement reduces to the [[Pythagorea
  6 KB (1,003 words) - 00:02, 20 May 2024
• Schur's Inequality
  ...Inequality''' is an [[inequality]] that holds for [[positive number]]s. It is named for Issai Schur. ...ath>a=b=c</math> or when two of <math>a,b,c</math> are equal and the third is <math>{0}</math>.
  2 KB (398 words) - 16:57, 29 December 2021
• Trigonometric identities
  ...<math>(\cos (x), \sin (x))</math> is defined to be on the unit circle, it is a distance one away from the origin. Then by the distance formula, <math>\s * <math>\sin 3x = 3\sin x-4\sin^3 x</math>
  8 KB (1,397 words) - 21:55, 20 January 2024
• Irrational number
  An '''irrational number''' is a [[real number]] that cannot be expressed as the [[ratio]] of two [[intege ...entury <math>B.C</math>. The Pythagoreans lived by the doctrine that ''all is number'', or that all things could be explained by relationships between nu
  3 KB (368 words) - 19:26, 6 June 2015
• Complex number
  ...ive]], so this equation has no solutions in the real numbers. However, it is possible to define a number, <math> i </math>, such that <math> i = \sqrt{- ...= \sqrt{-1} </math> is the [[imaginary unit]]. The set of complex numbers is denoted by <math>\mathbb{C}</math>. The set of complex numbers contains th
  5 KB (860 words) - 15:36, 10 December 2023
• Angle bisector
  ...math> such that the angle between this line and <math>\overline{AB}</math> is congruent to the angle between this line and <math>\overline{AC}</math>: D=(3,4);
  3 KB (575 words) - 15:27, 19 March 2023
• Without loss of generality
  ...ten abbreviated to WLOG, is a frequently used expression in math. The term is used to indicate that the following proof emphasizes on a particular case, If you use WLOG in a proof and the statement is not necessarily true, points will get marked off. For example, you can't sa
  2 KB (280 words) - 15:30, 22 February 2024
• Law of Sines
  The '''Law of Sines''' is a useful identity in a [[triangle]], which, along with the [[law of cosines ...math>, <math>c</math> opposite to <math>C</math>, and where <math>R</math> is the circumradius:
  4 KB (658 words) - 16:19, 28 April 2024
• Geometric sequence
  ...hat the ratio between any two consecutive terms is constant. This constant is called the '''common ratio''' of the sequence. ...mon ratio <math>-1/2</math>; however, <math>1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between c
  4 KB (644 words) - 12:55, 7 March 2022
• Arithmetic sequence
  ...he difference between any two consecutive terms is constant. This constant is called the '''common difference''' of the sequence. ...ence with common difference <math>1</math> and <math>99, 91, 83, 75</math> is an arithmetic sequence with common difference <math>-8</math>; however, <ma
  4 KB (736 words) - 02:00, 7 March 2024
• Fermat's Last Theorem
  ...ting that for positive [[integers]] <math>a,b,c,n</math> with <math>n \geq 3</math>, there are no solutions to the equation <math>a^n + b^n = c^n</math> ...vered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.''"
  3 KB (453 words) - 11:13, 9 June 2023
• 2005 USAMO Problems/Problem 4
  ...piece of length <math>k_i</math> from the end of leg <math>L_i \; (i = 1,2,3,4)</math> and still have a stable table? ...all four of the leg ends touch the floor. Note that a cut leg of length 0 is permitted.)
  7 KB (1,276 words) - 20:51, 6 January 2024
• 2000 AMC 12 Problems/Problem 1
  ...ger]]s such that the product <math>I \cdot M \cdot O = 2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? ...process on <math>2001</math> to get <math>667 * 3 * 1</math> as our <math>3</math> factors.
  2 KB (276 words) - 05:25, 9 December 2023
• Diophantine equation
  A '''Diophantine equation''' is an [[equation]] relating [[integer]] (or sometimes [[natural number]] or [[ ...a Diophantine equation has infinitely many solutions, [[parametric form]] is used to express the relation between the variables of the equation.
  9 KB (1,434 words) - 13:10, 20 February 2024
• Fraction
  A '''fraction''' is the [[ratio]] of two [[number]]s. Most commonly, we consider [[rational nu ...numerator is the same as the denominator such as <math>\frac{3}{3}</math> is always equal to <math>1</math>.
  3 KB (432 words) - 19:34, 11 June 2020
• Functional equation
  A '''functional equation''', roughly speaking, is an equation in which some of the unknowns to be solved for are [[function]] ...he '''inverse function'''.) Often the inverse of a function <math>f</math> is denoted by <math>f^{-1}</math>.
  2 KB (361 words) - 14:40, 24 August 2021
• Exponential form
  ...(yes, again!) rewrite <math>z</math> as <math>z=re^{i\theta}</math>, which is the general exponential form of a complex number. D=(1/2,sqrt(3)/2);
  1 KB (238 words) - 22:51, 20 February 2022
• Floor function
  ...ion is the same as "dropping everything after the decimal point," but this is ''not'' true for negative values. *<math>\lfloor 3.14 \rfloor = 3</math>
  3 KB (508 words) - 21:05, 26 February 2024
• Pascal's triangle
  '''Pascal's triangle''' is a triangle which contains the values from the [[binomial expansion]]; its v ...n</math>, the sum of the values on row <math>n</math> of Pascal's Triangle is <math>2^n</math>.
  5 KB (838 words) - 17:20, 3 January 2023
• Exponentiation
  .../math>, where <math>b</math> is the exponent (or power) and <math>a</math> is the [[base]]. ...ed if a equation has [[parentheses]] or the first one performed when there is no parentheses.
  5 KB (803 words) - 16:25, 10 August 2020

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