homothety

== English == === Etymology === From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”). === Pronunciation === === Noun === homothety (plural homotheties) (mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point. (commutative algebra, Bourbakist) A homomorphism from a module M {\displaystyle M} over a ring A {\displaystyle A} to itself of the form ν : x ↦ a x {\displaystyle \nu :x\mapsto ax} for some fixed a ∈ A {\displaystyle a\in A} (especially when M = A {\displaystyle M=A} ; a {\displaystyle a} is said to be the ratio of the homothety, by analogy with the geometric case). ==== Synonyms ==== (isotropic scaling transformation with a fixed point): homothecy, homogeneous dilation, homothetic transformation ==== Derived terms ==== ==== Related terms ==== homothetic ==== Translations ====