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Douglas Harper's Etymology Dictionary
isometry

1941, from Greek isometria "equality of measure," from iso- (see iso-) + metria "a measuring" (see -metry).

Wiktionary
isometry

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
isometry
  1. n. the growth rates in different parts of a growing organism are the same

  2. 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"

  3. equality of elevation above sea level

  4. equality of measure (e.g., equality of height above sea level or equality of loudness etc.)

Wikipedia
Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving injective map between metric spaces.

"We shall find it convenient to use the word transformation in the special sense of a one-to-one correspondence P → Pʹ among all points in the plane (or in space), that is, a rule for associating pairs of points, with the understanding that each pair has a first member and a second member and that every point occurs as the first member of just one pair and also as the second member of just one pair...

In particular, an isometry (or "congruent transformation," or "congruence") is a transformation which preserves length..." [[ Reflections with parallel axis on wallpaper.svg|thumb|upright=1.4|A composition of two opposite isometries is a direct isometry. A reflection in a line is an opposite isometry, like or on the image. Translation is a direct isometry: a rigid motion.

3.51 Any direct isometry is either a translation or a rotation. Any opposite isometry is either a reflection or a glide reflection.]]

Isometry (Riemannian geometry)

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, such a map is called an isometry (or isometric isomorphism), and provides a notion of isomorphism ("sameness") in the category Rm of Riemannian manifolds.

Isometry (disambiguation)

Isometry, in mathematics, refers to a distance-preserving transformation. Isometry may also refer to:

  • Isometry (quadratic forms)
  • Isometry (Riemannian geometry)
  • Isometry group
  • Quasi-isometry
  • Dade isometry
  • Euclidean plane isometry
  • Itō isometry