different between homothetic vs homothecy

English

Adjective

homothetic (not comparable)

1. (mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.
2. (mathematics) of a function of two or more variables in which the ratio of the partial derivatives depends only on the ratio of the variables, not their value
3. (economics) in which the ratio of goods demanded depends only on the ratio of their prices
4. the relationship of a microcosm to a macrocosm

Usage notes

According to the extension of Wu wei theory, ordering the Chinese Emperor's palace is governing the country well: the palace is an homothetic reproduction of the country.

Related terms

• homotheticity

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