Erlanger program

The Erlanger Programm, proposed by mathematician Felix Klein in 1872, unified the study of geometry. It defined geometry as the study of properties of a space that remain unchanged under a specific group of transformations.1

Klein's program suggested that different geometries, such as Euclidean and non-Euclidean, could be viewed as special cases of projective geometry. In this framework, a geometry consists of a "space" and a group of transformations. These transformations allow figures to be moved within the space without altering their fundamental characteristics. This approach unified various geometries and influenced mathematical developments by emphasizing the role of transformation groups.21