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• Cis
  ...hrm{cis}</math> is made up by the first letter of <math>\cos</math>, <math>i</math>, and the first letter of <math>\sin</math>. ...most always preferred to write <math>re^{i\theta}</math> rather than <math>r\mathrm{cis }(\theta)</math>, as [[Euler's formula]] states that
  1 KB (171 words) - 20:59, 11 July 2023
• Polar form
  ...n an [[angle]] <math>\theta</math> and a [[radius]] or [[magnitude]] <math>r</math>. ...s notation.) This represents a complex number <math>z</math> that is <math>r</math> units away from the origin, and <math>\theta</math> [[radian]]s coun
  633 bytes (105 words) - 13:35, 1 April 2022
• Roots of unity
  The '''Roots of unity''' are a topic closely related to [[trigonometry]]. Roots of unity come up when we e ...making <math>r^n=1\Rightarrow r=1</math> (magnitude is always expressed as a positive real number). This leaves us with <math>e^{ni\theta} = e^{2\pi ik
  3 KB (558 words) - 21:36, 11 December 2011
• Area
  ...size of the region that a two-[[dimension]]al figure occupies. The size of a region in higher dimensions is referred to as [[volume]]. It is often possible to find the area of a region bounded by parts of [[circle]]s and [[line segment]]s through elemen
  6 KB (1,181 words) - 22:37, 22 January 2023
• Exponential form
  ...> as <math>z=re^{i\theta}</math>, which is the general exponential form of a complex number. So <math>z=re^{i\theta}</math> looks like:
  1 KB (238 words) - 22:51, 20 February 2022
• Pascal's triangle
  ...ns the values from the [[binomial expansion]]; its various properties play a large role in [[combinatorics]]. ...2 is <math>{4 \choose 2} = 6</math>. Pascal's Triangle thus can serve as a "look-up table" for binomial expansion values. Also, many of the character
  5 KB (838 words) - 17:20, 3 January 2023
• Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
  ...power]], [[arithmetic mean]], [[geometric mean]], and [[harmonic mean]] of a set of [[positive]] [[real number]]s <math>x_1,\ldots,x_n</math> that says ..._1}+\cdots+\frac{1}{x_n}} \ge \sqrt[n_4]{\frac{x_1^{n_4}+\cdots+x_a^{n_4}}{a}}</cmath> where <math>n_1>1,~~0<n_2<1,~~-1<n_3<0,~~n_4<-1</math>, and <math
  5 KB (912 words) - 20:06, 14 March 2023
• Power of a Point Theorem
  ...e lengths of the [[line segment]]s formed when two [[line]]s [[intersect]] a [[circle]] and each other. ...of the lines is [[tangent line|tangent]] to the circle while the other is a [[secant line|secant]] (middle figure). In this case, we have <math> AB^2 =
  5 KB (827 words) - 17:30, 21 February 2024
• Fundamental Theorem of Algebra
  ...tant]] [[polynomial]] with [[complex number|complex]] [[coefficient]]s has a complex [[root]]. In fact, every known proof of this theorem involves some Suppose that <math>P(z)</math> is a complex polynomial of degree <math>n</math> with no complex roots; without
  5 KB (832 words) - 14:22, 11 January 2024
• Majorization
  ...l for all <math> 1 \le k \le n </math>, <math> \sum_{i=1}^{k}a_i \ge \sum_{i=1}^{k}b_i </math>, with equality when <math>k = n </math>. If <math>\{a_i\ ...y if for all <math> 1\le k \le n </math>, <math>\sum_{i=k}^n a_i \le \sum_{i=k}^n b_i</math>, with equality when <math>k=1 </math>. An interesting cons
  2 KB (288 words) - 22:48, 5 July 2023
• Algebraic geometry
  ...>. Then <math>V(I)=\{p\in\mathbb{A}^n\mid f(p)=0\mathrm{\ for\ all\ } f\in I\}</math> is called an '''affine algebraic variety'''. ...s are algebraic varieties. A projective space <math>\mathbb{P}^n</math> is a quotient set with an equivalence class satisfying
  2 KB (361 words) - 01:59, 24 January 2020
• Note that with two sequences <math>\mathbf{a}</math> and <math>\mathbf{b}</math>, and <math>\lambda_a = \lambda_b = 1/2< ...nces of nonnegative reals, and let <math>\{ \lambda_i \}_{i=1}^n</math> be a sequence of nonnegative reals such that <math>\sum \lambda = 1</math>. The
  4 KB (774 words) - 12:12, 29 October 2016
• Mock AMC
  ...an actual [[AMC]] (American Mathematics Competitions 8, 10, or 12) exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Prob == Tips for Writing a Mock AMC ==
  51 KB (6,175 words) - 20:58, 6 December 2023
• Modular arithmetic/Introduction
  ...is article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily ...ple, except let's replace the <math>12</math> at the top of the clock with a <math>0</math>.
  15 KB (2,396 words) - 20:24, 21 February 2024
• Convex function
  A convex function is a continuous function whose value at the midpoint of every interval in its do ...vex if for every <math> \lambda \in [0,1] </math> and every <math> x,y \in I</math>,
  2 KB (417 words) - 00:10, 20 February 2016
• Uncountable
  ...example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. == Proof that <math>\mathbb{R}</math> is uncountable ==
  2 KB (403 words) - 20:53, 13 October 2019
• Subset
  ...r than <math>B</math> itself. In the latter case, <math>A</math> is called a ''proper subset''. The following is a true statement:
  1 KB (217 words) - 09:32, 13 August 2011
• 2006 AIME I Problems
  {{AIME Problems|year=2006|n=I}} In quadrilateral <math> ABCD , \angle B </math> is a right angle, diagonal <math> \overline{AC} </math> is perpendicular to <mat
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AIME I Problems/Problem 13
  ...st integer <math> n </math> less than 1000 such that <math> S_n </math> is a [[perfect square]]. ...> is even, hence <math>k+n-1</math> is odd, and <math>S_n</math> cannot be a perfect square. Hence <math>k</math> must be even. In particular, as <math>
  10 KB (1,702 words) - 00:45, 16 November 2023
• LaTeX:Symbols
  This article provides a short list of commonly used LaTeX symbols. .../math> on the web, (technically an AJAX library simulating it.)) maintains a [http://docs.mathjax.org/en/latest/tex.html#supported-latex-commands list o
  16 KB (2,324 words) - 16:50, 19 February 2024

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