---
tag: 0J1N3WTKM4
kind: concept
name: Euclidean isometry
aliases: [rigid-transformation, euclidean-transformation]
msc: [51F20]
sources:
  - url: https://en.wikipedia.org/wiki/Euclidean_plane_isometry
    locator: Formal definition
  - url: https://en.wikipedia.org/wiki/Euclidean_group
    locator: lead section
---

## Summary

A Euclidean isometry is a map of a Euclidean space to itself that keeps the distance between each two points. Translations, rotations and reflections are examples. The Euclidean isometries of $\mathbb{R}^n$ form the Euclidean group.