different between transformation vs homothecy

English

Etymology

Borrowed from Middle French, from Ecclesiastical Latin tr?nsf?rm?ti?.Morphologically transform +? -ation

Pronunciation

• (US) IPA^(key): /?t?æns.f???me?.??n/
• (UK) IPA^(key): /?t?æns.f?(?)?me?.??n/
• Hyphenation: trans?for?ma?tion
• Rhymes: -e???n

Noun

transformation (countable and uncountable, plural transformations)

1. The act of transforming or the state of being transformed.
2. A marked change in appearance or character, especially one for the better.
3. (mathematics) The replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system.
4. (linguistics) A rule that systematically converts one syntactic form into another; a sentence derived by such a rule.
5. (genetics) The alteration of a bacterial cell caused by the transfer of DNA from another, especially if pathogenic.
6. (politics, South Africa) Ideologically driven government policy - becoming more conformant with socialist and African nationalist groupthink.

Synonyms

• metamorphosis
• transmogrification
• transmutation
• transfiguration

Derived terms

• transformational

Related terms

• transform
• Lorentz transformation

Translations

French

Etymology

Borrowed from Ecclesiastical Latin tr?nsf?rm?ti?, tr?nsf?rm?ti?nem, from Latin tr?nsf?rm?.

Pronunciation

• IPA^(key): /t???s.f??.ma.sj??/

Noun

transformation f (plural transformations)

1. transformation
2. (rugby) conversion

Derived terms

• transformation de Fourier

Related terms

• transformer (verb)

Further reading

• “transformation” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Swedish

Noun

transformation c

1. transformation

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