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• Spiral similarity
  ....</math> The line <math>\ell</math> is symmetrical to <math>SC</math> with respect to <math>AB</math> and intersects <math>BC</math> at <math>D.</math> Prove Points <math>D</math> and <math>D'</math> are simmetric with respect <math>AB,</math> so <math>BD = BD' \implies k = \frac {SC}{SB} = \frac {BC}
  28 KB (4,863 words) - 00:29, 16 December 2023
• 1975 USAMO Problems/Problem 2
  ...math> is a function of <math>\theta</math>, so we take the derivative with respect to <math>\theta</math> and obtain that <math>a^2+b^2</math> takes a minimum ...spond to the position vectors of points A, B, C, and D, respectively, with respect to an arbitrary origin O. Let us also for simplicity define <math>a^2 = a \
  6 KB (1,096 words) - 23:07, 26 August 2017
• 1989 AJHSME Problems/Problem 11
  ...h of the five "T-like shapes" would be [[symmetric]] to the one shown with respect to the dashed line?
  2 KB (192 words) - 22:27, 9 November 2015
• Polynomial ring
  This operator <math>\partial</math> is called the ''(formal) derivative (with respect to <math>x</math>)'', and behaves much like the [[derivative]] of a functio
  12 KB (2,010 words) - 00:10, 3 August 2020
• 1989 AJHSME Problems
  Which of the five "T-like shapes" would be symmetric to the one shown with respect to the dashed line?
  13 KB (1,765 words) - 11:55, 22 November 2023
• Radical axis
  The '''power''' of point <math>P</math> with respect to circle <math>\omega</math> (with radius <math>r</math> and center <math> ...h>P</math> such that the [[power of a point|power]] of <math>P</math> with respect to <math>\omega_1</math> and <math>\omega_2</math> are equal. In other word
  12 KB (2,125 words) - 08:38, 23 May 2024
• 2009 AIME II Problems/Problem 15
  ...1+\tan (\alpha)} - 1</math>. Taking the derivative of <math>VW</math> with respect to <math>\alpha</math>, we arrive at ...math>t</math> (and the constant <math>a</math>). Differentiating this with respect to <math>t</math> yields
  11 KB (1,862 words) - 21:23, 23 May 2024
• 2009 USAMO Problems/Problem 5
  ...= BD \cap TQ</math>, <math>R</math> and <math>R'</math> are symmetric with respect to the axis of symmetry of trapezoid <math>ABCD</math>. This implies that l
  6 KB (973 words) - 19:24, 18 October 2018
• Fundamental group
  ...a(t)</math>, which is "compatible" with the concatenation in the following respect:
  8 KB (1,518 words) - 20:11, 23 January 2017
• Euclidean space
  ...ematical objects. For example, Euclidean space is a [[metric space]] with respect to the [[distance formula|distance]] [[metric]], <math>d(\bold{x},\bold{y})
  1,018 bytes (164 words) - 12:46, 13 March 2010
• Linearly independent
  Any [[eigenvector]]s corresponding to different [[eigenvalue]]s (with respect to a linear map <math>L</math>) are linearly independent. This can be prove
  2 KB (300 words) - 23:35, 16 March 2010
• AXA Achievement Scholarship
  * Respect for self, family and community
  818 bytes (107 words) - 16:12, 14 June 2010
• 2010 IMO Problems/Problem 4
  Now consider the power of point <math>S</math> with respect to <math>\Gamma</math>.
  6 KB (895 words) - 18:32, 2 April 2021
• 2019 IMO Problems/Problem 6
  An inversion with respect <math>\omega</math> swap <math>A</math> and <math>A' \implies A'</math> is ...ga</math> meet on the polar line of the intersection of the diagonals with respect to <math>\omega \implies DI</math> and <math>PS</math> meet on the line thr
  5 KB (792 words) - 01:52, 19 November 2023
• Mobius function
  Let <math>f(n)</math> be a multiplicative function with respect to <math>n</math>. If there is such an <math>f</math>, then
  5 KB (910 words) - 02:58, 1 March 2022
• 2011 AMC 12A Problems
  ...peed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock <math>B</math> downriver, then im
  13 KB (1,994 words) - 13:52, 3 July 2021
• 2011 AMC 12A Problems/Problem 12
  ...peed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock <math>B</math> downriver, then im .../math> distance apart in the third diagram when they meet. Therefore, with respect to each other, the boat and the raft cover a distance of <math>d</math> on
  5 KB (928 words) - 23:01, 14 April 2022
• 2011 AIME II Problems/Problem 10
  ...<math>PB</math> and <math>PA</math>). Then, by Power of a Point on P with respect to the circle with center <math>O</math>, we have that
  11 KB (1,720 words) - 03:12, 18 December 2023
• 2011 USAMO Problems/Problem 5
  ...h>AD</math> or <math>BC</math> depending on where <math>R</math> is). With respect to triangle <math>BCR</math>, <math>P</math> and <math>Q_1</math> are isogo
  4 KB (660 words) - 01:04, 15 February 2024
• 2015 IMO Problems/Problem 4
  ...nd and the third chords are anti-parallel to the first (common) chord with respect to the given lines, so they are parallel to each other. <math>\Box</math><b
  3 KB (502 words) - 23:58, 5 October 2015

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