Combinatorial Geometry

A complete, self-contained introduction to a powerful and resurging mathematical discipline … Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Tóth, Rogers, and Erd???s. Nearly half the results presented in this book were discovered over the past twenty years, and most have never before appeared in any monograph. Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design. It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery of the material. Topics covered include:Geometric number theoryPacking and covering with congruent convex disksExtremal graph and hypergraph theoryDistribution of distances among finitely many pointsEpsilon-nets and Vapnik—Chervonenkis dimensionGeometric graph theoryGeometric discrepancy theoryAnd much more