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• Number theory/Advanced
  ...s a function such that for all <math>z\in\mathcal{H}</math> and all <math>\gamma\in SL_2(\mathbb{Z})</math> we have <cmath>f(\gamma z)=(cz+d)^{-k}f(z)</cmath>
  5 KB (849 words) - 15:14, 18 May 2021
• Real number
  ...any value. Some examples of real numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are <math>\ 3i</math>, We see that <math>S'</math> is a cut, say <math>\gamma</math>
  3 KB (496 words) - 22:22, 5 January 2022
• Complex analysis
  ...ed Jordan curve]]. Then for any <math>z_0</math> in the interior of <math>\Gamma</math>, we have <cmath> f^{(n)}(z_0)=\frac{n!}{2\pi i} \oint_\Gamma \frac{f(z)\; dz}{(z-z_0)^{n+1}}. </cmath>
  2 KB (271 words) - 21:06, 12 April 2022
• Riemann zeta function
  <math>\frac{\pi^2}{6}</math>. Euler also found that since every number is the product <cmath>\xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma\left(\frac s2\right)\zeta(s).</cmath>
  9 KB (1,547 words) - 02:04, 13 January 2021
• LaTeX:Symbols
  ...th>\alpha</math>||\alpha||<math>\beta</math>||\beta||<math>\gamma</math>||\gamma||<math>\delta</math>||\delta |<math>\pi</math>||\pi||<math>\varpi</math>||\varpi||<math>\rho</math>||\rho||<math>\varrho</math>
  16 KB (2,315 words) - 19:35, 4 November 2024
• Newman's Tauberian Theorem
  Let <math>\Gamma</math> be the counterclockwise contour on the boundary <cmath> F(0)-F_T(0) = \frac{1}{2\pi i} \int_\Gamma K(z) (F(z)-F_T(z))
  6 KB (1,034 words) - 06:55, 12 August 2019
• 1989 AIME Problems
  pair A=(0,0),B=(10,0),C=6*expi(pi/3); ...des of a triangle, and let <math>\alpha</math>, <math>\beta</math>, <math>\gamma</math>, be the angles opposite them. If <math>a^2+b^2=1989c^2</math>, find
  7 KB (1,045 words) - 19:47, 14 December 2023
• 2006 Cyprus MO/Lyceum/Problem 19
  ...figure, <math>AB\Gamma</math> is an [[isosceles triangle]] with<math> AB=A\Gamma=\sqrt2</math> and <math>\angle A=45^\circ</math>. If <math>B\Delta</math> i ...ight)\qquad\mathrm{(C)}\ \frac{8\sqrt2-3\pi}{16}\qquad\mathrm{(D)}\ \frac{\pi}{8}\qquad\mathrm{(E)}\ \text{None of these}</math>
  1 KB (214 words) - 22:44, 22 December 2016
• 2008 AMC 12B Problems
  ...uad \textbf{(C)}\ \pi \qquad \textbf{(D)}\ 2\pi \qquad \textbf{(E)}\ 10^{2\pi}</math> ...are both real. What is the smallest possible value of <math>| \alpha | + |\gamma |</math>?
  14 KB (2,199 words) - 12:43, 28 August 2020
• 2010 USAMO Problems/Problem 3
  \frac{\Gamma(\frac{5}{4}) \Gamma(\frac{5}{2}) \Gamma(\frac{9}{4})} {\Gamma(\frac{11}{4}) \Gamma(\frac{3}{2}) \Gamma(\frac{7}{4})}\cdot
  11 KB (1,889 words) - 12:45, 4 July 2013
• 1966 IMO Problems
  ...ly, the angles opposite these sides. Prove that if <cmath> a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta}) </cmath> the triangle is isosceles. ...ural number <math>n</math>, and for every real number <math>x \neq \frac{k\pi}{2^t}</math> (<math>t=0,1, \dots, n</math>; <math>k</math> any integer)
  3 KB (509 words) - 11:39, 29 January 2021
• 2019 IMO Problems/Problem 6
  We define <math>\angle MID = \beta, \angle MDI = \gamma \implies</math> <math>\angle IMA = \angle MID + \angle MDI = \beta + \gamma = \varphi.</math>
  5 KB (792 words) - 00:52, 19 November 2023
• 1969 IMO Problems
  Given that <math>f(x_1) = f(x_2) = 0</math>, prove that <math>x_2 - x_1 = m\pi</math> for some integer <math>m</math>. ...nd <math>\gamma_3</math> are both tangent to <math>CD</math> and to <math>\gamma</math>, one on each side of <math>CD</math>. Prove that <math>\gamma_1</mat
  3 KB (428 words) - 12:34, 29 January 2021
• LaTeX Cheat Sheet
  ...\phi, \Delta, \Omega, \omega represents <math>\alpha, \beta, \gamma, \pi, \Pi, \phi, \Delta, \Omega, \omega</math> respectively
  2 KB (318 words) - 12:47, 4 May 2024
• 1966 IMO Problems/Problem 2
  .../math> be the lengths of the sides of a triangle, and <math> \alpha,\beta,\gamma </math> respectively, the angles opposite these sides. Prove that if <cmath> a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta}), </cmath>
  6 KB (1,009 words) - 19:17, 10 November 2024
• 2012 AIME II Problems/Problem 15
  ...iameter <math>\overline{DE}</math>. Circles <math>\omega</math> and <math>\gamma</math> meet at <math>E</math> and a second point <math>F</math>. Then <math ...d. Note that the midpoint <math>M</math> of <math>BC</math> lies on <math>\gamma</math>, and <math>BC</math> and <math>\omega</math> are swapped. Thus point
  15 KB (2,516 words) - 16:28, 17 September 2024
• 2013 USAMO Problems/Problem 1
  Use directed angles modulo <math>\pi</math>. ...\angle BAC=\alpha,</math> <math>\angle ABC=\beta,</math> <math>\angle ACB=\gamma,</math> and let <math>\angle APB=\theta.</math> We construct lines through
  14 KB (1,830 words) - 17:22, 10 May 2023
• 1967 IMO Problems/Problem 4
  ...nt <math>P</math> inside <math>A_0B_0C_0</math> s.t. <math>\angle X_0PY_0=\pi-\angle X_1Z_1Y_1</math>, where <math>X,Y,Z</math> are a permutation of <mat <math>\frac{A_0B}{\sin (\pi - B - \alpha)} = \frac{b_0}{\sin B}</math>, and a
  9 KB (1,690 words) - 19:22, 10 November 2024
• 1994 AHSME Problems
  ...qquad\textbf{(C)}\ 4\pi-4 \qquad\textbf{(D)}\ 2\pi+4 \qquad\textbf{(E)}\ 4\pi-2 </math> ...l be between two students. In how many ways can Professors Alpha, Beta and Gamma choose their chairs?
  14 KB (2,124 words) - 12:39, 19 February 2020
• 2014 AIME I Problems/Problem 15
  ...we can find from angle chasing that <math>\angle ABF = \angle EDF = \frac{\pi}4</math>. Therefore, <math>\overline{BF}</math> is the angle bisector of <m ...>\angle GED = \angle GCD =\gamma \implies \overset{\Large\frown} {DG} = 2\gamma.</cmath>
  10 KB (1,654 words) - 17:53, 24 November 2024

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