Erlangen program

The Erlangen Program, developed by mathematician Felix Klein in 1872, is a way of understanding geometric shapes and their properties through symmetries. It classifies geometries based on the groups of transformations—such as rotations, reflections, and translations—that leave certain properties unchanged. Instead of focusing solely on shapes themselves, it emphasizes the role of symmetry groups in defining and distinguishing different geometrical systems. This approach unified various branches of geometry, providing a deeper understanding of how shapes behave under transformations and highlighting the structural essence of geometric concepts.