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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.
Download as PDF; Printable version ... is an undergraduate mathematics textbook on finite geometry by Lynn ... the many types of geometry covered in the book, ...
92 Finite Group Theory, I. Martin Isaacs (2008, ISBN 978-0-8218-4344-4) 93 Topics in Differential Geometry , Peter W. Michor (2008, ISBN 978-0-8218-2003-2 ) 94 Representations of Semisimple Lie Algebras in the BGG Category O , James E. Humphreys (2008, ISBN 978-0-8218-4678-0 )
The Fano plane, the projective plane over the field with two elements, is one of the simplest objects in Galois 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]
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 ...
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.
In finite geometry, PG(3, 2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane. It has 15 points, 35 lines, and 15 planes. [1] It also has the following properties: [2] Each point is contained in 7 lines and 7 planes. Each line is contained in 3 planes and contains 3 points.
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).