Meaning of homothety | Babel Free

Definitions

1. An isotropic scaling transformation of an affine space with a single fixed point.
2. 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).

Equivalents

Examples

“The product of two homotheties with the same centre is a homothety with that centre.”

“One cannot obtain⟳ all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.”

“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.”

CEFR level