Etymology
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isometry (n.)

in mathematics, 1941, probably from isometric (q.v.) on the model of geometry/geometric.

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Definitions of isometry

isometry (n.)
the growth rates in different parts of a growing organism are the same;
isometry (n.)
a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points;
isometry (n.)
equality of elevation above sea level;
isometry (n.)
equality of measure (e.g., equality of height above sea level or equality of loudness etc.);
From wordnet.princeton.edu