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Benz plane

In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: Möbius planes, Laguerre planes, and Minkowski planes.[1] [2]

Planar circle geometries or Benz planes[edit]

Because of the essential role of the circle (considered as the non-degenerate conic in a projective plane) and the plane description of the original models the three types of geometries are subsumed to planar circle geometries or in honor of Walter Benz, who considered these geometric structures from a common point of view, Benz planes.

Conformal geometry

Quadric

Projective plane

Laguerre transformations

Francis Buekenhout (1981) "Les plans de Benz", Journal of Geometry 17(1):61–8.

from Encyclopedia of Mathematics

Benz plane

Erich Hartmann from Darmstadt University of Technology

Planar Circle Geometries, an Introduction to Moebius-, Laguerre- and Minkowski Planes