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...

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...

homothetic or homothety in Wiktionary, the free dictionary. Homothetic may refer to: Homothetic transformation, also known as homothety, homothecy, or...

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...

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...

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...

reflection is equivalent to a special case of homothetic transformation: homothety with homothetic center coinciding with P, and scale factor −1. (This is...

transformations: a homothety, an isometry, and a special conformal transformation. For linear transformations, a conformal map may only be composed of homothety and...

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...

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...

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...

mathematical morphology Scaling (geometry), including: Homogeneous dilation (homothety), the scalar multiplication operator on a vector space or affine space...

{\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...

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...

case, the geometrical similarity becomes a homothety and the thermal center is the center of the homothety itself. The thermal center does not always...

rotations and reflections transform a figure into congruent figures; homotheties — into similar figures. For example, all circles are mutually similar...

reflections Translation Glide reflection Similarity Similarity transformation Homothety Shear mapping 2D computer graphics 2D geometric model Altitude Brahmagupta's...

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...

projective transformations of a line is generated by the translations, the homotheties, and the multiplicative inversion. The differences z j − z k {\displaystyle...

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...

center of dilation. Some congruences have fixed points and others do not. Homothety Dilation (operator theory) Montgomery, Richard (2002), A tour of subriemannian...

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...

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...

Euclidean geometry, uniform scaling (isotropic scaling, homogeneous dilation, homothety) is a linear transformation that enlarges (increases) or shrinks (diminishes)...

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...

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...

Some other names for dilation are uniform scaling, isotropic scaling, homothety, and homothecy. The study of triangle centers traditionally is concerned...

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 ⁡...

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...

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...