noun ·Rare ·Advanced level

Definitions

Noun

1. 1
   An 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."

2. 2
   (mathematics) an isotropic scaling transformation of an affine space with a single fixed point. wordnet
3. 3
   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).

Synonyms

All synonyms

homothecyenlargementhomogeneous dilationhomothecyhomothetic transformation

Example

More examples

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

Etymology

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

Related phrases

roto-homothetyaffine spacefixed point

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.