** Next:** 2.1 Formulas for Symmetries in Cartesian Coordinates
**Up:** Part I: Two-Dimensional Geometry
** Previous:** 1.5 Oblique Coordinates in the Plane

A transformation of the plane (invertible map of the plane to itself) that
preserves distances is called an **isometry** of the plane. Every
isometry of the plane is of one of the following types:

- the
**identity**(which leaves every point fixed); - a
**translation**by a vector**v**; - a
**rotation**through an angle around a point*P*; - a
**reflection**in a line*L*; - a
**glide-reflection**in a line*L*with displacement*d*.

- 2.1 Formulas for Symmetries in Cartesian Coordinates
- 2.2 Formulas for Symmetries in Homogeneous Coordinates
- 2.3 Formulas for Symmetries in Polar Coordinates
- 2.4 Wallpaper Groups

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.