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homothety

noun

Etymology

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

Definitions

  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.
    • 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.

  2. A homomorphism from a module M over a ring A to itself of the form ν

    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).

The neighborhood

Derived

roto-homothety

Vish — recursive loop

No curated loop yet for homothety. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA