homothety

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English

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A homothety

Etymology

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

Noun

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homothety (plural homotheties)

  1. (mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.
    • 1927, Henry George Forder, The Foundations of Euclidean Geometry[1], page 178:
      The product of two homotheties with the same centre is a homothety with that centre.
    • 1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:
      One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.
    • 2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:
      Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by hP,λ the homothety with center P and similitude ratio λ.
  2. (commutative algebra, Bourbakist) A homomorphism from a module over a ring to itself of the form for some fixed (especially when ; is said to be the ratio of the homothety, by analogy with the geometric case).

Synonyms

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Translations

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