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Home > Art, Film & Photography > Configurations: Mbius-Kantor Graph, Desargues' Theorem, Configuration, Fano Plane, Heawood Graph, Tutte-Coxeter Graph, Gray Graph
Configurations: Mbius-Kantor Graph, Desargues' Theorem, Configuration, Fano Plane, Heawood Graph, Tutte-Coxeter Graph, Gray Graph

Configurations: Mbius-Kantor Graph, Desargues' Theorem, Configuration, Fano Plane, Heawood Graph, Tutte-Coxeter Graph, Gray Graph


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Mbius-kantor Graph, Desargues' Theorem, Configuration, Fano Plane, Heawood Graph, Tutte-coxeter Graph, Gray Graph, Mbius Configuration, Levi Graph, Complete Quadrangle, Pappus Graph. Excerpt: A complete quadrangle (at left) and a complete quadrilateral (at right). In mathematics, specifically projective geometry, a complete quadrangle is a projective configuration (4362) consisting of four points, no three of which are collinear, and the six lines defined by those four points. This configuration was called a tetrastigm by Lachlan (1893), and that term is occasionally still used. The projective dual configuration (6243) to a complete quadrangle is a complete quadrilateral (called a tetragram by Lachlan), a configuration consisting of four lines, no three of which pass through a common point, and the six points of intersection of those four lines. The six lines of a complete quadrangle meet in pairs to form three additional points beyond the four defining the configuration; it is one of the fundamental axioms of projective geometry that these three points can never be collinear (Coxeter 1987: 15). For any two complete quadrangles, or any two complete quadrilaterals, there is a unique projective transformation taking one of the two configurations into the other (Coxeter 1987: 51). Wells (1991) describes several additional properties of complete quadrilaterals that involve metric properties of the Euclidean plane, rather than being purely projective. The six points of a complete quadrilateral form three pairs of points that are not already connected by lines; the line segments connecting these pairs are called diagonals . The midpoints of the diagonals are collinear, and (as proved by Isaac Newton ) also collinear with the center of a conic tangent to the lines of the quadrila...


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Product Details
  • ISBN-13: 9781155548630
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Mbius-Kantor Graph, Desargues' Theorem, Configuration, Fano Plane, Heawood Graph, Tutte-Coxeter Graph, Gray Graph
  • Width: 229 mm
  • ISBN-10: 1155548639
  • Publisher Date: 05 May 2010
  • Binding: Paperback
  • Spine Width: 3 mm
  • Weight: 86 gr


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