Laguerre planeIn mathematics, a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Laguerre planes are named after the French mathematician Edmond Nicolas Laguerre. The classical Laguerre plane is an incidence structure that describes the incidence behaviour of the curves , i.e. parabolas and lines, in the real affine plane. In order to simplify the structure, to any curve the point is added.
Minkowski planeIn mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane). Applying the pseudo-euclidean distance on two points (instead of the euclidean distance) we get the geometry of hyperbolas, because a pseudo-euclidean circle is a hyperbola with midpoint . By a transformation of coordinates , , the pseudo-euclidean distance can be rewritten as . The hyperbolas then have asymptotes parallel to the non-primed coordinate axes.
Finite geometryA finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity.
Conformal geometryIn mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale.
