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Isometry

This article is about distance-preserving functions. For other mathematical uses, see isometry (disambiguation). For non-mathematical uses, see Isometric.
Not to be confused with Isometric projection.
A composition of two opposite isometries is a direct isometry. A reflection in a line is an opposite isometry, like R 1 or R 2 on the image. Translation T is a direct isometry: a rigid motion.[1]

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.[a] The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion.

  1. ^ Coxeter 1969, p. 46

    3.51 Any direct isometry is either a translation or a rotation. Any opposite isometry is either a reflection or a glide reflection.
  2. ^ Coxeter 1969, p. 29


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