Benz plane

Summary

Benz plane is the common name for three kinds of circle geometry: Möbius planes, Laguerre planes and Minkowski planes. Each kind is an incidence structure of points and circles in which three suitable points lie on exactly one circle and circles can touch. The classical examples are the plane sections of a sphere, of a circular cylinder and of a hyperboloid of one sheet. The name honours Walter Benz, who developed their common theory.