isometry
(aɪˈsɒmɪtrɪ)
[ad. Gr. ἰσοµετρία equality of measure (f. µέτρος measure): see -y3.]
1. Math. A one-to-one transformation of one metric space into another that preserves the distances or metrics between each pair of points.
| 1941 Birkhoff & MacLane Survey Mod. Algebra vi. 128 An obvious example is furnished by the symmetries of the cube. Geometrically speaking, these are the one–one transformations which preserve distances on the cube. They are known as ‘isometries’, and are 48 in number. 1965 S. Lang Algebra xiv. 356 If σ is a linear isomorphism, and is metric, then we say that σ is an isometry. 1966 J. H. Cadwell Topics in Recreational Math. xi. 113 A fundamental property of isometries is that any two carried out in succession define a third. Thus if isometry U takes figure F into figure F{p}, while V takes F{p} into F{pp}, their combined effect, taken in this order, is an isometry carrying F into F{pp}. |
2. Biol. = isogony (s.v. isogonic a.2).
| 1950 J. S. Huxley in Proc. R. Soc. B. CXXXVII. 465 Isometry is used of the special case when the organ grows at the same rate as the body. |