Motion (geometry)

In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion.

Motions can be divided into direct (also known as proper or rigid) and indirect (or improper) motions. Direct motions include translations and rotations, which preserve the orientation of a chiral shape. Indirect motions include reflections, glide reflections, and Improper rotations, that invert the orientation of a chiral shape. Some geometers define motion in such a way that only direct motions are motions.

More generally, the term motion is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. In the latter case, hyperbolic motions provide an approach to the subject for beginners.

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