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Definitions:
Noun
isometry
Definition: the growth rates in different parts of a growing organism are the same
isometry
Definition: a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points; "the isometries of the cube"
isometry
Definition: equality of elevation above sea level
isometry
Definition: equality of measure (e.g., equality of height above sea level or equality of loudness etc.)
Definition: A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.