In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and...
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a rotation and a homothety. Similarity and rotation have the same angle of +135 degrees modulo 360 degrees. Similarity and homothety have the same ratio...
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homothetic or homothety in Wiktionary, the free dictionary. Homothetic may refer to: Homothetic transformation, also known as homothety, homothecy, or...
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combined with a homothety and a translation, shear mapping combined with a homothety and a translation, or squeeze mapping combined with a homothety and a translation...
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Menelaus's theorem (section A proof using homotheties)
notions of affine geometry, notably homotheties. Whether or not D, E, F are collinear, there are three homotheties with centers D, E, F that respectively...
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for all s, Schur's lemma implies that A ( u ) {\displaystyle A(u)} is a homothety λ I n {\displaystyle \lambda I_{n}} . Its trace nλ is equal to ∑ s ∈ G...
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reflection is equivalent to a special case of homothetic transformation: homothety with homothetic center coinciding with P, and scale factor −1. (This is...
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transformations: a homothety, an isometry, and a special conformal transformation. For linear transformations, a conformal map may only be composed of homothety and...
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point A where A is the center of the homothety, and a number k that represents the ratio of the homothety, a homothety is a transformation that will move...
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that a homothetic copy R of r is circumscribed about C and the positive homothety ratio is at most 2 and 0.5 × Area ( R ) ≤ Area ( C ) ≤ 2 × Area ( r...
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of which the graph is a line through the origin. More generally, any homothety v ↦ c v {\textstyle \mathbf {v} \mapsto c\mathbf {v} } centered in the...
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mathematical morphology Scaling (geometry), including: Homogeneous dilation (homothety), the scalar multiplication operator on a vector space or affine space...
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{\displaystyle r} is circumscribed about C {\displaystyle C} and the positive homothety ratio is at most 2 and 0.5 × Area ( R ) ≤ Area ( C ) ≤ 2 × Area ( r...
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circle's center. Further, a conical surface is invariant as a set under a homothety of space. An invariant set of an operation T is also said to be stable...
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case, the geometrical similarity becomes a homothety and the thermal center is the center of the homothety itself. The thermal center does not always...
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rotations and reflections transform a figure into congruent figures; homotheties — into similar figures. For example, all circles are mutually similar...
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reflections Translation Glide reflection Similarity Similarity transformation Homothety Shear mapping 2D computer graphics 2D geometric model Altitude Brahmagupta's...
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that must be specified. However, it does uniquely characterize it up to homothety, meaning up to bijections that only change the notion of distance by an...
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projective transformations of a line is generated by the translations, the homotheties, and the multiplicative inversion. The differences z j − z k {\displaystyle...
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the identity. (A scalar multiple of the identity is sometimes called a homothety.) Proof: Suppose f {\displaystyle f} is a nonzero G-linear map from V...
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center of dilation. Some congruences have fixed points and others do not. Homothety Dilation (operator theory) Montgomery, Richard (2002), A tour of subriemannian...
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subalgebra, isomorphic to the Lie algebra of Hom(2), the group of euclidean homotheties, X 1 , X 2 , X 4 {\displaystyle X_{1},X_{2},X_{4}} generate a Bianchi...
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onto the equatorial plane described above, and a homothety from it to the polar plane. The homothety scales the image by a factor of 2 (a ratio of a diameter...
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Euclidean geometry, uniform scaling (isotropic scaling, homogeneous dilation, homothety) is a linear transformation that enlarges (increases) or shrinks (diminishes)...
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homothety and a rotation. If | a | = 1 {\displaystyle |a|=1} then it is a rotation, if a ∈ R {\displaystyle a\in \mathbb {R} } then it is a homothety...
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X ∈ TM \ {0} and λ > 0. Here d(Sλ) is the pushforward along the scalar homothety S λ : X ↦ λ X . {\displaystyle S_{\lambda }:X\mapsto \lambda X.} A particular...
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Some other names for dilation are uniform scaling, isotropic scaling, homothety, and homothecy. The study of triangle centers traditionally is concerned...
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that a homothetic copy R of r is circumscribed about C. The positive homothety ratio is at most 2 and: 1 2 ⋅ Area ( R ) ≤ Area ( C ) ≤ 2 ⋅ Area ...
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represented by a matrix A that is a scalar times an orthogonal matrix. Thus homothety is added, self-similarity is considered a symmetry. The group of affine...
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observe that MN becomes CZ under a clockwise rotation of 30° around A and a homothety of ratio 3 {\displaystyle {\sqrt {3}}} with the same center, and that...
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