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searching for Homothety 38 found (50 total)

alternate case: homothety

Affine transformation (3,594 words) [view diff] exact match in snippet view article find links to article

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

Point reflection (2,573 words) [view diff] exact match in snippet view article find links to article

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

Burnside's theorem (1,208 words) [view diff] exact match in snippet view article find links to article

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

Homothetic vector field (112 words) [view diff] exact match in snippet view article find links to article

physics, a homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition: L X g a b

Constructions in hyperbolic geometry (1,901 words) [view diff] exact match in snippet view article find links to article

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

Johnson circles (1,255 words) [view diff] exact match in snippet view article find links to article

obtained from the Johnson triangle by a homothety with factor 2, it follows from composition of homotheties that the reference triangle is homothetic

Fubini–Study metric (5,289 words) [view diff] exact match in snippet view article find links to article

subgroup U(n+1) in GL(n+1,C). A Fubini–Study metric is determined up to homothety (overall scaling) by invariance under such a U(n+1) action; thus it is

DrGeo (1,496 words) [view diff] exact match in snippet view article find links to article

one of these transformations: reflexion symmetry translation rotation homothety Dr. Geo comes with macro-construction: a way to teach Dr. Geo new constructions

Thermal center (404 words) [view diff] exact match in snippet view article find links to article

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

Projective vector field (1,079 words) [view diff] exact match in snippet view article find links to article

As ∇ h = 0 {\displaystyle \nabla h=0} , every homothety is an affine and the set of all homotheties on M {\displaystyle M} forms a Lie subalgebra of

Menelaus's theorem (1,488 words) [view diff] exact match in snippet view article find links to article

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

Convex polygon (881 words) [view diff] exact match in snippet view article find links to article

{\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

Clifton–Pohl torus (748 words) [view diff] exact match in snippet view article find links to article

d y x 2 + y 2 {\displaystyle g={\frac {2\,dx\,dy}{x^{2}+y^{2}}}} Any homothety is an isometry of M {\displaystyle M} , in particular including the map:

Conformal map (2,511 words) [view diff] exact match in snippet view article find links to article

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

Fibonacci word fractal (1,098 words) [view diff] exact match in snippet view article find links to article

different ways (see gallery below): Iterated function system of 4 and 1 homothety of ratio 1 / ( 1 + 2 ) {\displaystyle 1/(1+{\sqrt {2}})} and 1 / ( 1 +

Outline of geometry (912 words) [view diff] exact match in snippet view article find links to article

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

Rectangle (2,162 words) [view diff] exact match in snippet view article find links to article

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

Medial triangle (878 words) [view diff] exact match in snippet view article find links to article

triangle can also be viewed as the image of triangle △ABC transformed by a homothety centered at the centroid with ratio -1/2. Thus, the sides of the medial

Hyperbolic space (1,538 words) [view diff] exact match in snippet view article find links to article

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

Homothetic center (2,817 words) [view diff] exact match in snippet view article find links to article

easily proven that triangles △O1PQ, △O2P'Q' are similar because of the homothety. They are also isosceles because O 1 P ¯ = O 1 Q ¯ {\displaystyle {\overline

Napoleon's theorem (2,876 words) [view diff] exact match in snippet view article find links to article

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 LN

Schur's lemma (3,883 words) [view diff] exact match in snippet view article find links to article

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

Möbius transformation (10,549 words) [view diff] exact match in snippet view article find links to article

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

Moduli stack of elliptic curves (2,342 words) [view diff] exact match in snippet view article find links to article

\wp '(z,\Lambda ),1]\in \mathbb {P} ^{2}(\mathbb {C} )} and holds up to homothety of the lattice Λ {\displaystyle \Lambda } , which is the equivalence relation

Clawson point (432 words) [view diff] exact match in snippet view article find links to article

trinagle Centers (ETC) LE POINT CLAWSON PAR LES TRIANGLES ORTHIQUES ET EXTANGENT Clawson Point: Orthic Triangle, Extangents Triangle, Homothecy or Homothety

Convex set (3,037 words) [view diff] exact match in snippet view article find links to article

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 ⁡

Geodesic (3,684 words) [view diff] exact match in snippet view article find links to article

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

Invariant (mathematics) (2,729 words) [view diff] exact match in snippet view article

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

2D computer graphics (3,986 words) [view diff] exact match in snippet view article find links to article

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

Utility functions on divisible goods (199 words) [view diff] exact match in snippet view article find links to article

Demand curve Indirect utility Indifference curves Monotonicity Convexity Homothety Good type Example Leontief min ( x w x , y w y ) {\displaystyle \min \left({x

Semilinear map (2,059 words) [view diff] exact match in snippet view article find links to article

\sigma } is an inner automorphism of R {\displaystyle R} . Thus, the homothety x ↦ α x {\displaystyle x\mapsto \alpha x} need not be a linear map, but

Discriminant (6,665 words) [view diff] exact match in snippet view article find links to article

projective transformation may be decomposed into a product of translations, homotheties and inversions, this results in the following formulas for simpler transformations

Triangle center (3,898 words) [view diff] exact match in snippet view article find links to article

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

Symmetry (geometry) (3,471 words) [view diff] exact match in snippet view article

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

Cross-ratio (4,680 words) [view diff] exact match in snippet view article find links to article

projective transformations of a line is generated by the translations, the homotheties, and the multiplicative inversion. The differences zj − zk are invariant

Space (mathematics) (9,319 words) [view diff] exact match in snippet view article

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

Waldspurger formula (2,532 words) [view diff] exact match in snippet view article find links to article

(G)}=A^{0}} . De facto, there is only one such A 0 {\displaystyle A^{0}} modulo homothety. Let T 1 , T 2 {\displaystyle T_{1},T_{2}} be two maximal tori of G {\displaystyle

Representation theory of finite groups (21,307 words) [view diff] exact match in snippet view article find links to article

= ρ 2 , {\displaystyle \rho _{1}=\rho _{2},} F {\displaystyle F} is a homothety (i.e. F = λ Id {\displaystyle F=\lambda {\text{Id}}} for a λ ∈ C {\displaystyle