homothety
Collocations
3VERB + HOMOTHETY
center, centre
HOMOTHETY + NOUN
p
PREP.
with
Definitions
noun
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.
One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.
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).
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Example Bank
3The product of two homotheties with the same centre is a homothety with that centre.
WiktionaryOne cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.
WiktionarySince 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.
Wiktionary