Matousek J. Introduction to Discrete Geometry 2003

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Matousek J. Introduction to Discrete Geometry 2003

Textbook in PDF format Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object. Department of Applied Mathematics. Convexity Linear and Affine Subspaces, General Position Convex Sets, Convex Combinations, Separation Radon’s Lemma and Helly’s Theorem Centerpoint and Ham Sandwich Lattices and Minkowski’s Theorem Minkowski’s Theorem General Lattices An Application in Number Theory Convex Independent Subsets The Erdős–Szekeres Theore Horton Sets Incidence Problems Formulation Lower Bounds: Incidences and Unit Distance Point–Line Incidences via Crossing Numbers Convex Polytopes Geometric Duality H-Polytopes and V -Polytopes Faces of a Convex Polytope Many Faces: The Cyclic Polytopes The Upper Bound Theorem Voronoi Diagrams Number of Faces in Arrangements Arrangements of Hyperplanes Arrangements of Other Geometric Objects Number of Vertices of Level at Most k The Zone Theore