12 Groups and Geometry

Erlangen Program

With the rise of non-Euclidean geometries in the 1800’s, the mathematics community approached the study of geometry from several different perspectives. F. Klein (1872) created a new method of characterizing a geometry based on the group structure of the group of transformations, and the properties that are invariant under them. It is named the Erlangen program after the university where Felix Klein was a professor.

References

Klein, F. (1872). Vergleichende betrachtungen ber neuere geometrische forschungen. Andreas Deichart.