isometryn.
/ʌɪˈsɒmɪtri/ 1. Mathematics. A one-to-one transformation of one metric space into another that preserves the distances or metrics between each pair of points.
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements
inclusion1870
orthomorphosis1885
isomorphism1892
identity1910
homoeomorphism1918
homomorphism1935
topological mapping or transformation1939
isometry1941
Möbius transformation1941
injection map(ping)1950
monomorphism1954
bijection1963
surjection1964
1941 G. Birkhoff & S. MacLane Surv. 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′, while V takes F′ into F″, their combined effect, taken in this order, is an isometry carrying F into F″.
2. Biology. = isogony n. at isogonic adj.2 Derivatives.
ΘΚΠ
the world > life > biology > biological processes > development, growth, or degeneration > [noun] > growth > rates of growth
heterauxesis1886
heterogony1927
growth-gradient1929
isogony1932
allometry1936
isometry1950
1950 J. S. Huxley in Proc. Royal Soc. B. 137 465 Isometry is used of the special case when the organ grows at the same rate as the body.
This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2018).
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n.1941