Dictionary

homothety en · NOUN

Pronunciation

• (US) audio

Etymology

From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).

Meanings

1. An isotropic scaling transformation of an affine space with a single fixed point.
   • One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities. 1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:
   • Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ. 2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:
   • The product of two homotheties with the same centre is a homothety with that centre. 1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:
2. (qualifier:commutative algebra) A homomorphism from a module M over a ring A to itself of the form ν:x↦ax for some fixed a∈A (especially when M=A; a is said to be the ratio of the homothety, by analogy with the geometric case).

Forms

Deriveds

roto-homothety

Relateds

homothetic

Synonyms

homothetic transformation (isotropic scaling transformation with a fixed point) · homothecy (isotropic scaling transformation with a fixed point) · homogeneous dilation (isotropic scaling transformation with a fixed point)

Translations (9)

gl homotecia (scaling transformation) · it omotetia (scaling transformation) · eo homotetio (scaling transformation) · fr homothétie (scaling transformation) · pl homotetia (scaling transformation) · pt homotetia (scaling transformation) · es homotecia (scaling transformation) · pl jednokładność (scaling transformation) · de zentrische Streckung (scaling transformation)