transformation (geometry)

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set. Specifically, "A geometric transformation is a function whose domain and range are sets of points. Most often the domain and range of a geometric transformation are both R² or both R³. Often geometric transformations are required to be 1-1 functions, so that they have inverses." The study of geometry may be approached via the study of these transformations.

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic approach to the study of geometry by focusing on groups of geometric transformations, and the properties of figures that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on geometric constructions.