Equality of measure

• Equality of elevation above sea level
• Distance-preserving transformation, as the rotation of a plane
• Equality of measure turns to misery

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1941, from Greek isometria "equality of measure," from iso- (see iso- ) + metria "a measuring" (see -metry ).

Wiktionary Word definitions in Wiktionary
n. (context mathematics English) 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.

WordNet Word definitions in WordNet
n. the growth rates in different parts of a growing organism are the same 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" equality of elevation above ...

Wikipedia Word definitions in Wikipedia
In the study of Riemannian geometry in mathematics , a local isometry from one ( pseudo -) Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism ...