Erlangen program

Summary

The Erlangen program is a view of geometry that Felix Klein stated in 1872. In it, a geometry is the study of the properties of a space that are invariant under a given group of transformations. Euclidean, affine and projective geometry then differ only in their groups: the Euclidean group, the affine group and the projective group. A larger group has fewer invariants, so projective geometry has fewer theorems than affine geometry, which has fewer than Euclidean geometry.