homothety

plural homotheties

1. geometryAn isotropic scaling transformation of an affine space with a single fixed point.

   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 more examples

   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

   Synonyms: homothecy, homogeneous dilation, homothetic transformation

2. commutative algebraA 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).