Definition:Erlangen Program/Historical Note

Historical Note on Erlangen Program
The Erlangen program was published by in $1872$ in his.

It is named after the, where worked.

By $1872$, non-Euclidean geometries had emerged.

However, nothing had been done to determine their hierarchy and relationships.

's approach was as follows:


 * Projective geometry was identified as the unifying frame for all other geometries considered by him. Hence the following hierarchy was developed:
 * Affine geometry was more restrictive than projective geometry
 * Euclidean geometry was more restrictive than affine geometry.


 * proposed that group theory was the most useful way of organizing geometrical knowledge, emerging from the discipline of Galois theory.


 * specificially identified the appropriate geometrical language in which to define the relevant concepts for each level of the hierarchy.