homothety
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English[edit]
Etymology[edit]
From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).
Noun[edit]
homothety (plural homotheties)
- (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.
Synonyms[edit]
- (isotropic scaling transformation with a fixed point): homothecy, homogeneous dilation, homothetic transformation