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  • ...e can study the set of points where both coordinates lie in some subfield (like the reals or the rationals). One also needs to add a limit point, called th ...ve, they can be added in a way that satisfies the normal laws of addition, like associativity, commutativity and the existence of an identity and inverses.
    5 KB (849 words) - 15:14, 18 May 2021
  • and as a public service, I re-write the proof below. ...of <math>\angle A, \angle B, \angle C, \angle D</math> is <math>\ge \frac{\pi}{2}</math>
    6 KB (1,054 words) - 17:09, 11 December 2024
  • ...an ellipse with semimajor and semiminor axes <math>a,b</math> is <math>ab\pi</math>. ...re relatively prime positive integers. Find <math>m+n</math>. ([[2001 AIME I Problems/Problem 5|Source]])
    5 KB (892 words) - 20:52, 1 May 2021
  • ...mber]], as proved by Lindemann in 1882) denoted by the Greek letter <math>\pi </math>. ...^2}=\frac{\pi^2}{6}</math>. Some common [[fraction]]al approximations for pi are <math>\frac{22}{7} \approx 3.14285</math> and <math>\frac{355}{113} \ap
    8 KB (1,469 words) - 20:11, 16 September 2022
  • ..., we have <math>\ln (-1)=i\pi</math>. Additionally, <math>\ln (-n)=\ln n+i\pi</math> for positive real <math>n</math>.
    4 KB (680 words) - 11:54, 16 October 2023
  • ...as a positive real number). This leaves us with <math>e^{ni\theta} = e^{2\pi ik}</math>. ...math> ni\theta = 2\pi ik</math>. Solving this gives <math> \theta=\frac{2\pi k}n </math>. Additionally, we note that for each of <math> k=0,1,2,\ldots,
    3 KB (558 words) - 20:36, 11 December 2011
  • <cmath> f^{(n)}(z_0)=\frac{n!}{2\pi i} \oint_\Gamma \frac{f(z)\; dz}{(z-z_0)^{n+1}}. </cmath> Let <math>f</math> be an [[entire]] function (i.e. holomorphic on the whole complex plane). If <math>\lvert f(z)\rvert \le
    2 KB (271 words) - 21:06, 12 April 2022
  • ...th>. Then an equivalent statement of the Riemann hypothesis is that <math>\pi(x)=\mathrm{Li}(x)+O(x^{1/2}\ln(x))</math>. ...tion]] to <math>\Re(s)>\frac{1}{2}</math>. Let <math>M(n)=\sum_{i=1}^n \mu(i)</math> be the [[Mertens function]]. It is easy to show that if <math>M(n)\
    2 KB (425 words) - 02:18, 29 June 2024
  • ...ic is called a [[transcendental number]], such as <math>e</math> or <math>\pi</math>.
    1 KB (153 words) - 11:30, 27 September 2024
  • specifically, it states that the functions <math>\pi(x)</math> and <math>x/\log x</math> are [[asymptotically equivalent]], where <math>\pi(x)</math> is the number
    10 KB (1,729 words) - 18:52, 21 October 2023
  • ...texify] is an online application which allows you to draw the symbol you'd like and shows you the <math>\text{\LaTeX}</math> code for it! |<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
  • ...can <math>|\pi - |e - | e - \pi|||</math> be expressed in terms of <math>\pi</math> and <math>e?</math> ...}2\pi-2e\qquad\textbf{(C) }2e\qquad\textbf{(D) }2\pi \qquad\textbf{(E) }2\pi +e</math>
    12 KB (1,784 words) - 15:49, 1 April 2021
  • (i) <math>f(1) = 1</math>, and ...rt3}{2} \qquad \text {(D) } \frac {10\pi}{3} - \sqrt3 \qquad \text {(E) }4\pi - 2\sqrt3</math>
    13 KB (1,953 words) - 23:31, 25 January 2023
  • ...that is, <math>A > B > C</math>, <math>D > E > F</math>, and <math>G > H > I > J</math>. Furthermore, ...</math> are consecutive even digits; <math>G</math>, <math>H</math>, <math>I</math>, and <math>J</math> are consecutive odd
    13 KB (1,957 words) - 11:53, 24 January 2024
  • ...{C}) 75+100\pi \quad (\mathrm {D}) 100+100\pi \quad (\mathrm {E}) 100+125\pi</math> ...hrm{(C) \ } \pi c^2 \qquad \mathrm{(D) \ } \pi d^2 \qquad \mathrm{(E) \ } \pi e^2 </math>
    13 KB (2,049 words) - 12:03, 19 February 2020
  • \mathrm{(A)}\ 80-20\pi \qquad \mathrm{(B)}\ 60-10\pi \qquad
    12 KB (1,781 words) - 13:59, 19 July 2024
  • ...z_{n}}</math> is the [[complex conjugate]] of <math>z_{n}</math> and <math>i^{2}=-1</math>. Suppose that <math>|z_{0}|=1</math> and <math>z_{2005}=1</ma Since <math>|z_0|=1</math>, let <math>z_0=e^{i\theta_0}</math>, where <math>\theta_0</math> is an [[argument]] of <math>z_
    5 KB (802 words) - 22:50, 25 July 2024
  • MP('I', (8,-8), (0,0)); ...qquad\mathrm{(D)} \text{II, by}\ 8\pi\qquad\mathrm{(E)}\ \text{II, by}\ 10\pi</math>
    13 KB (2,028 words) - 15:32, 22 March 2022
  • MP('I', (8,-8), (0,0)); ...{(D) } II,\,\textrm{ by }\,8\pi\qquad \textbf{(E) } II,\,\textrm{ by }\,10\pi </math>
    3 KB (424 words) - 09:14, 17 December 2021
  • <cmath> F(0)-F_T(0) = \frac{1}{2\pi i} \int_\Gamma K(z) (F(z)-F_T(z)) \le\int_{\Gamma_+} \frac{2M}{R^2} \lvert dz \rvert = \frac{2\pi M}{R} . </cmath>
    6 KB (1,034 words) - 06:55, 12 August 2019

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