Euclidean Plane Isometry

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below under classification of Euclidean plane isometries).

The set of Euclidean plane isometries forms a group under composition: the Euclidean group in two dimensions. It is generated by reflections in lines, and every element of the Euclidean group is the composite of at most three distinct reflections.

Read more about Euclidean Plane Isometry:  Informal Discussion, Formal Definition, Classification of Euclidean Plane Isometries, Isometries As Reflection Group, Isometries in The Complex Plane

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