Laguerre plane

In mathematics, a Laguerre plane is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane, named after the French mathematician Edmond Nicolas Laguerre.

Essentially the classical Laguerre plane is an incidence structure which describes the incidence behaviour of the curves ${\displaystyle y=ax^{2}+bx+c}$ , i.e. parabolas and lines, in the real affine plane. In order to simplify the structure, to any curve ${\displaystyle y=ax^{2}+bx+c}$ the point ${\displaystyle (\infty ,a)}$ is added. A further advantage of these completion is: The plane geometry of the completed parabolas/lines is isomorphic to the geometry of the plane sections of a cylinder (s. below).

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