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• Inverse with respect to an operation
  30 bytes (3 words) - 11:39, 23 November 2007

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• Pythagorean Theorem
  ...considering the [[Power of a Point | power of point]] <math>A </math> with respect to <math>\omega </math>, we see
  5 KB (886 words) - 21:12, 22 January 2024
• Physics
  * The rate of change of momentum of a body with respect to time is directly proportional to the force acting on it.
  9 KB (1,355 words) - 07:29, 29 September 2021
• Cyclic quadrilateral
  * Any two opposite sites of the quadrilateral are antiparallel with respect to the other two opposite sites.
  1 KB (162 words) - 20:39, 9 March 2024
• Riemann sum
  The '''Riemann sum''' of <math>f</math> with respect to <math>\mathcal{\dot{P}}</math> on <math>[a,b]</math> is defined as <math The '''Upper sum''' of <math>f</math> with respect to <math>\mathcal{P}</math> on <math>[a,b]</math> is defined as <math>U(f,\
  1 KB (272 words) - 12:06, 7 May 2008
• Henstock-Kurzweil integral
  .../math> is the [[Riemann sum]] of <math>f</math> on <math>[a,b]</math> with respect to <math>\mathcal{\dot{P}}</math>
  2 KB (401 words) - 09:46, 31 January 2018
• Pi
  Integrating <math>n</math> times by parts with respect to <math>x</math>, we see that our integral equals <math>\iint_{(0,1)\times
  8 KB (1,469 words) - 21:11, 16 September 2022
• Homothety
  ...'') is a transformation of space which [[dilation|dilates]] distances with respect to a fixed point. A homothety can be an enlargement (resulting figure is l ...itionally, <math>ABCD</math> and <math>A'B'C'D'</math> are homothetic with respect to <math>O</math>.
  3 KB (532 words) - 01:11, 11 January 2021
• Trigonometry
  ...f trigonometry involves the ratios between edges of a right triangle, with respect to a given angle. The definitions below will be referring to angle <math>A<
  8 KB (1,217 words) - 20:15, 7 September 2023
• Power of a Point Theorem
  .../math> must be a circle. If we consider the lines and <math>P</math> with respect simply to that circle, then we have reduced our claim to the case of two di
  5 KB (827 words) - 17:30, 21 February 2024
• Mathematicial notation
  is the "Hilbert symbol of <math>a,b</math> in respect to <math>v</math>" (nontrivial means here that not all numbers are <math>0<
  8 KB (1,401 words) - 13:11, 17 June 2008
• Algebraic geometry
  ...are algebraic varieties given as open subsets of a projective variety with respect to the Zariski topology.
  2 KB (361 words) - 01:59, 24 January 2020
• Algebraic topology
  ...a(t)</math>, which is "compatible" with the concatenation in the following respect:
  3 KB (479 words) - 15:35, 1 December 2015
• 2005 AMC 12B Problems/Problem 7
  The graph is symmetric with respect to both coordinate axes, and in the first quadrant it coincides with the gr
  2 KB (357 words) - 20:15, 27 December 2020
• 2005 AIME II Problems/Problem 14
  ==Solution 5 (Isogonal lines with respect to A angle bisesector)== Since <math>AE</math> and <math>AD</math> are isogonal with respect to the <math>A</math> angle bisector, we have <cmath>\frac{BE}{EC}\cdot \fr
  13 KB (2,129 words) - 18:56, 1 January 2024
• 1983 AIME Problems/Problem 11
  ...th>l=6\sqrt{2}+\sqrt{2}h</math> since it similarly increases linearly with respect to <math>h</math>. Now we solve:<cmath>\int_0^6(6\sqrt{2}-\sqrt{2}h)(6\sqrt
  5 KB (865 words) - 21:11, 6 February 2023
• 1984 AIME Problems/Problem 15
  ...}{a-5^2}+\frac{w^2}{a-7^2}=1</math>. We can let this be a polynomial, with respect to <math>a</math>. We can say that <math>w^2</math>, <math>x^2</math>, <mat
  6 KB (1,050 words) - 18:07, 16 January 2024
• 1986 AIME Problems/Problem 2
  ...this solution, note that the original expression has cyclic symmetry with respect to <math>x,y,</math> and <math>z:</math>
  3 KB (460 words) - 00:44, 5 February 2022
• 1996 AIME Problems/Problem 7
  ...re isn't occupied and the two squares that are opposite to each other with respect to the center square, in which there are <math>12</math> cases. ...ach other with a <math>90^{\circ}</math> rotation with each other and with respect to the center square, in which case there are <math>12</math> cases.
  4 KB (551 words) - 11:44, 26 June 2020
• 1997 AIME Problems/Problem 12
  ...ath> and <math>97</math>, we know that the involution is an inversion with respect to a circle with a diameter from <math>19</math> to <math>97</math>. The on
  11 KB (2,063 words) - 22:59, 21 October 2023
• 1998 AIME Problems/Problem 9
  ...\frac{2m}{60}</math>, depending upon the location of <math>M_1</math> with respect to the endpoints. Intuitively, the average probability will occur at <math>
  4 KB (624 words) - 18:34, 18 February 2018
• 2000 AIME I Problems/Problem 13
  ...at <math>(x,0)</math>. All these circles are [[homothety|homothetic]] with respect to a center at <math>(5,0)</math>.
  3 KB (571 words) - 00:38, 13 March 2014
• 2001 AIME I Problems/Problem 5
  Since the triangle is symmetric with respect to the y-axis, the coordinates of <math>B</math> and <math>C</math> are now
  6 KB (1,043 words) - 10:09, 15 January 2024
• 2003 AIME I Problems/Problem 11
  Note that the three expressions are symmetric with respect to interchanging <math>\sin</math> and <math>\cos</math>, and so the probab
  2 KB (284 words) - 13:42, 10 October 2020
• Negative number
  * [[Inverse with respect to an operation]]
  635 bytes (93 words) - 14:07, 16 January 2023
• Centroid
  ...spectively. Hence the triangles <math>ABC, DEF</math> are homothetic with respect to some point <math>G</math> with dilation factor <math>-\frac{1}{2}</math>
  3 KB (612 words) - 22:32, 25 February 2024
• Group
  ...>g^{-1}\in G</math> so that <math>gg^{-1}=g^{-1}g=e</math> ([[Inverse with respect to an operation | inverses]]).
  2 KB (365 words) - 12:03, 12 November 2023
• Inverse
  * [[Inverse with respect to an operation]], such as in a [[group]] (see also [[identity]])
  334 bytes (52 words) - 11:42, 23 November 2007
• Holomorphic function
  ...all the [[partial derivative]]s of <math>u</math> and <math>v</math> with respect
  9 KB (1,537 words) - 21:04, 26 July 2017
• Dedekind domain
  ...t <math>M_f</math> be the [[matrix]] representation of <math>f</math> with respect to <math>x_1,\ldots,x_m</math>. Then <math>M_f</math> is an <math>m\times m
  9 KB (1,648 words) - 16:36, 14 October 2017
• Operation
  * [[Inverse with respect to an operation]]
  357 bytes (54 words) - 09:17, 18 July 2006
• Vector space
  ...ity]] (usually denoted <math>\mathbf 0</math>) and additive [[inverse with respect to an operation | inverses]].
  3 KB (561 words) - 00:47, 21 March 2009
• Mock AIME 1 2006-2007 Problems/Problem 5
  ...to the following: "If <math>n</math> has a multiplicative [[inverse with respect to an operation | inverse]] [[mod]] <math>p</math>, <math>f_p(n)</math> is
  2 KB (340 words) - 15:52, 3 April 2012
• Mock AIME 1 2006-2007 Problems/Problem 7
  ...<math>BF</math> is 1. We can now use Menelaus on line <math>DF</math> with respect to triangle <math>ABC</math>:
  3 KB (518 words) - 16:54, 25 November 2015
• 1973 IMO Shortlist Problems/Bulgaria 1
  ...nce the [[power of a point | power]] of <math>\displaystyle P </math> with respect to <math>\displaystyle S </math> is invariant, we may multiply both sides o
  2 KB (346 words) - 14:59, 30 July 2006
• Derivative
  ...]] is defined as the instantaneous [[rate]] of change of the function with respect to one of the [[variable]]s. Note that not every function has a derivative
  509 bytes (64 words) - 19:26, 3 March 2010
• Reciprocal
  ...any non-zero element of a [[field]]) is its multiplicative [[inverse with respect to an operation | inverse]]. The reciprocal is usually denoted <math>r^{-1
  554 bytes (87 words) - 11:43, 23 November 2007
• Integral
  ...(f,\mathcal{\dot{P}})</math> is the [[Riemann sum]] of <math>f</math> with respect to <math>\mathcal{\dot{P}}</math> ...emann sum|lower sum]] and [[Riemann sum|upper sum]] of <math>f</math> with respect to [[partition]] <math>\mathcal{P}</math>
  5 KB (909 words) - 14:16, 31 May 2022
• Free group
  The [[inverse with respect to an operation | inverse]] of a given element of a free group can be found
  2 KB (454 words) - 17:54, 16 March 2012
• Monoid
  ...natively, a monoid can be thought of as a [[group]] without [[inverse with respect to an operation | inverses]], or as an associative [[magma]] with an identi ...ebra]], and many objects (such as all groups, as well as any [[ring]] with respect to either of its operations) are in fact monoids.
  3 KB (670 words) - 22:45, 21 May 2008
• Euler line
  Let <math>\omega'</math> be the circle symmetric to <math>\omega</math> with respect to <math>AB.</math> Let <math>E</math> be the point symmetric to <math>O</math> with respect to <math>AB.</math>
  59 KB (10,203 words) - 04:47, 30 August 2023
• Special relativity
  ...t moving in the direction of motion of earth should have moved slower with respect to the earth than light moving in the opposite direction, as everything had
  3 KB (538 words) - 23:39, 2 March 2008
• Skew field
  ...ommutative) ring in which every [[element]] has a two-sided [[inverse with respect to an operation | inverse]]. Equivalently, a skew field is a [[field]] in
  1 KB (253 words) - 19:05, 9 September 2008
• Quaternion
  ...t is, a [[ring]] in which each element has a multiplicative [[inverse with respect to an operation | inverse]]; alternatively, a non[[commutative]] [[field]])
  1,007 bytes (155 words) - 20:47, 14 October 2013
• Canada/USA Mathcamp
  ...thcamp officially has only four rules (generally invoking common sense and respect). Students have the freedom and flexibility to choose what classes and act
  4 KB (680 words) - 23:22, 12 April 2021
• Totally ordered set
  ...natural" ordering of this set. In particular, it behaves very poorly with respect to arithmetic operations on <math>\mathbb C</math>.
  1 KB (174 words) - 12:52, 25 November 2007
• 2005 IMO Shortlist Problems/G1
  ...of <math> \displaystyle D </math> and <math> \displaystyle E </math> with respect to <math> \displaystyle I </math>. Prove that the quadrilateral <math> \di ...yle T </math> to the circumcircle of <math> \displaystyle ABC </math> with respect to lines <math> \displaystyle AC, PT </math> gives us <center> <math> \frac
  7 KB (1,088 words) - 16:57, 30 May 2007
• 2004 IMO Shortlist Problems/G2
  By considering the power of the point <math> \displaystyle D </math> with respect to <math> \displaystyle \Gamma </math>, we see <math> \displaystyle DE^2 =
  10 KB (1,539 words) - 23:37, 6 June 2007
• Circumradius
  Circumradius and altitude are isogonals with respect bisector and vertex of triangle.
  4 KB (729 words) - 16:52, 19 February 2024
• Chicken McNugget Theorem
  ...every integer point <math>T</math>, the reflection of <math>T</math> with respect to <math>P</math> is an integer point of a different colour than <math>T</m
  17 KB (2,748 words) - 19:22, 24 February 2024
• Implicit differentiation
  ...[[derivative|differentiating]] both sides of an implicit [[equation]] with respect to one of the [[variable]]s. The [[dependent variable]] is treated as a [[f
  757 bytes (125 words) - 01:04, 26 March 2018

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