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• 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
• 2007 AMC 12A Problems/Problem 22
  ...designed to be satisfied except whether <math>S(n)</math> is accurate with respect to <math>n.</math> So, the only thing that remains is to check this. We may
  15 KB (2,558 words) - 19:33, 4 February 2024
• 2006 AIME II Problems/Problem 12
  ..., and <math>EF=13</math>. If we take a homothety of the parallelogram with respect to <math>A</math>, such that <math>F</math> maps to <math>G</math>, we see
  6 KB (1,033 words) - 02:36, 19 March 2022
• Asymptote: CSE5
  ''S'' allows you to position the label manually with respect to the middle point of the largest arc. The automatic positioning is where
  4 KB (607 words) - 15:09, 30 June 2020
• De Longchamps point
  ...ymmetrical to the point of intersection of the heights <math>H</math> with respect to <math>O.</math> ...<math>C-</math>power cicles is symmetric to altitude <math>AH</math> with respect <math>O.</math>
  10 KB (1,780 words) - 09:23, 17 November 2022
• Construction
  16. Construct the inverse of a point P with respect to circle C. In other words, construct the unique point <math>P'</math> on
  3 KB (443 words) - 20:52, 28 August 2014
• 1990 USAMO Problems/Problem 5
  Now we use the Power of a Point theorem with respect to point <math>H</math>. From the circle with diameter <math>AB</math> we g
  3 KB (604 words) - 20:52, 24 October 2018
• Isogonal conjugate
  '''Isogonal conjugates''' are pairs of [[point]]s in the [[plane]] with respect to a certain [[triangle]]. ...l</math> and containing the point <math>O</math> be called isogonals with respect to the pair <math>(\ell,O).</math>
  54 KB (9,416 words) - 08:40, 18 April 2024
• 2008 AMC 12A Problems/Problem 25
  ...the origin by <math>30^\circ</math> and dilating the point's position with respect to the origin by a factor of <math>2</math>.
  5 KB (745 words) - 10:58, 9 December 2022
• Symmetric group
  ...ect to subgroups, just as [[free group]]s can be considered universal with respect to [[quotient group]]s.
  10 KB (1,668 words) - 15:33, 25 May 2008
• Mock AIME 1 2007-2008 Problems/Problem 14
  The [[Law of Cosines]] on <math>\triangle BAO</math> with respect to <math>\angle BAO</math> yields ...sqrt{11}</math>. The [[Law of Cosines]] on <math>\triangle CAO</math> with respect to <math>\angle CAO</math> yields
  2 KB (375 words) - 15:23, 25 November 2009
• 2008 AIME II Problems/Problem 5
  ...then <math>BC</math> and <math>AD</math> are [[homothecy|homothetic]] with respect to point <math>E</math> by a ratio of <math>\frac{BC}{AD} = \frac{125}{251}
  8 KB (1,338 words) - 23:15, 28 November 2023
• Complement
  ...subset; in this case, we speak of the ''complement of <math>X</math> with respect to <math>A</math>''. Such a set is sometimes denoted <math>\overline{X}</m
  748 bytes (135 words) - 14:22, 9 April 2008
• 2008 AIME II Problems/Problem 13
  ...'ll see that the problem's basically asking you to invert the hexagon with respect to the unit circle in the Cartesian Plane using the Inversion Distance Form
  6 KB (894 words) - 18:56, 25 December 2022
• Fiber product
  ...ategory. Then the fiber product of <math>X</math> and <math>Y</math> with respect to <math>Z</math>, denoted <math>X \times_Z Y</math> (when the specific fun
  770 bytes (131 words) - 21:55, 7 September 2008
• Quotient set
  ...lence relation. The set of [[equivalence class]]es of <math>S</math> with respect to <math>\mathcal{R}</math> is called the ''quotient of <math>S</math> by < ...pect to <math>\mathcal{R}</math>. The ''saturation of <math>A</math> with respect to <math>\mathcal{R}</math>'' is the least saturated subset <math>A'</math>
  2 KB (358 words) - 09:42, 7 June 2016
• Coset
  ...ft cosets of <math>H</math> is called the ''index'' of <math>H</math> with respect to <math>G</math>; it is denoted <math>(G:H)</math>. This is also the card
  4 KB (897 words) - 01:28, 3 September 2008
• Restricted sum
  ...ndices <math>i</math> is the ''restricted sum of the <math>G_i</math> with respect to the <math>H_i</math>''. ...[trivial group |trivial]], the restricted sum of the <math>G_i</math> with respect to the <math>H_i</math> is again the direct sum of the <math>G_i</math>. W
  1 KB (273 words) - 13:07, 6 June 2008
• Mechanics
  *The rate of change of momentum of a body with respect to time is directly proportional to the force acting on it.
  2 KB (309 words) - 15:41, 1 December 2015
• 2003 USAMO Problems/Problem 4
  ...math>. This exact condition can also be visualized through power of M with respect to the circumcircle of triangle <math>BDC</math> and getting the angle cond
  5 KB (820 words) - 02:39, 10 January 2023
• 1995 IMO Problems/Problem 1
  ...XY</math> of the original two circles, so the power of <math>Z</math> with respect to each of the four circles is all equal to <math>ZM * ZA</math>. Hence, <m
  5 KB (847 words) - 19:03, 12 October 2021

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