different between homothety vs homothecy

English

Etymology

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

Noun

homothety (plural homotheties)

1. (mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.
   • 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 ?, we shall denote by h_P,? the homothety with center P and similitude ratio ?.

Synonyms

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

Related terms

• homothetic

Translations

English

Noun

homothecy (plural homothecies)

1. (geometry) A homothetic transformation.
   • 1950, Duke Mathematical Journal, Duke University Press, page 76,

     Let us determine the center and the ratio of this homothecy.

   • 1981, Kenneth Joseph Arrow, Michael D. Intriligator, Handbook of Mathematical Economics, North-Holland, page 1720,

     The restriction of B to S_b is a homothecy of scale b.

   • 2013, Felipe Cucker, Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press, page 161,

     Proposition 7.4 Homothecies preserve circles. That is, for any homothecy h and any circle C, h(C) is a circle as well. […] Were we willing to do the same with homothecies, we would meet an obstruction: the composition of two homothecies is not necessarily a homothecy.

Synonyms

• (type of transformation): homogeneous dilation, homothety

Translations