homothety

English

A homothety

Etymology

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

Noun

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, 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 h_P,λ the homothety with center P and similitude ratio λ.

Synonyms

• (isotropic scaling transformation with a fixed point): homothecy, homogeneous dilation, homothetic transformation

Related terms

• homothetic

Translations

scaling transformation

• Galician: homotecia (gl) f
• Italian: omotetia (it) f
• (deprecated template usage) {{trans-mid}}
• Polish: jednokładność f, homotetia f