Transformations, Symmetries, and Tilings

Rigid motion of plane

A transformation of the plane

Transformation of the Plane

A one-to-one set correspondence of the set of points in the plane onto itself.

Four Basic Rigid Motions

Translations

AKA slide, all points of the plane are moved the same distance in the same direction.

Rotaions

AKA turn, one point is held fixed and the remaining points are turned about the center of the rotation the same number of degrees.

Reflections

AKA flip, a reflection is determined by a line in the plane.

Glide-Reflections

Combines both a slide and reflection.