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A 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.
The types of finite geometry covered by the book include partial linear spaces, linear spaces, affine spaces and affine planes, projective spaces and projective planes, polar spaces, generalized quadrangles, and partial geometries. [1]
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help. Pages in category "Finite geometry" The following 14 ...
A frequently studied problem in finite geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a ...
Affine geometry can be viewed as the geometry of an affine space of a given dimension n, coordinatized over a field K. There is also (in two dimensions) a combinatorial generalization of coordinatized affine space, as developed in synthetic finite geometry .
Galois geometry (named after the 19th-century French mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field). [1] More narrowly, a Galois geometry may be defined as a projective space over a finite field. [2]
locally finite if closures of finite sets are finite. Triviality, modularity and local modularity pass to the associated geometry and are preserved under localization. If S {\displaystyle S} is a locally modular homogeneous pregeometry and a ∈ S ∖ cl ( ∅ ) {\displaystyle a\in S\setminus {\text{cl}}(\varnothing )} then the localization of ...
The upper half plane model of n+1 dimensional hyperbolic space in R n+1 projects to R n, and the inverse image of P under this projection is a geometrically finite polyhedron with an infinite number of sides. A geometrically finite polyhedron has only a finite number of cusps, and all but finitely many sides meet one of the cusps.