Transformation geometry - Definition and Overview

In mathematics, transformation geometry is a name for a pedagogic theory for teaching Euclidean geometry, based on the Erlangen programme. Felix Klein who put forward that point of view was himself much interested in mathematical education. It took many years, though, for his "modern" point of view to have much effect, with the synthetic geometry point of view remaining dominant.

In the end, reform of geometry teaching came simultaneously with the rest of the New Math movement, over much of the West. To do real transformation geometry requires some facility with symmetry groups; if not group theory, matrix computations are required. The tide of transformation geometry retreated, leaving behind some vector methods.