different between isotropic vs homothety

English

Etymology

From iso- +? -tropic, from Ancient Greek ???? (ísos, “equal”) + ???????? (tropikós, “of or pertaining to a turn or change; or the solstice; or a trope or figure; tropic; tropical; etc.”).

Adjective

isotropic (not comparable)

1. (physics) Having properties that are identical in all directions; exhibiting isotropy
2. (mathematics) Having the same components in all rotated coordinate systems

Antonyms

• anisotropic

Related terms

• coisotropic
• isotrope
• isotropism
• isotropy
• semiisotropic

Translations

See also

• omnidirectional

Further reading

• isotropic in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• isotropic in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• isotropic at OneLook Dictionary Search

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