Combinatorial Geometry

Combinatorial Geometry

Author(s): János Pach, Pankaj K. Agarwal

Published Online: 28 OCT 2011 10:27AM EST

Print ISBN: 9780471588900

Online ISBN: 9781118033203

DOI: 10.1002/9781118033203

About this Book

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 Toth, 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 theory
* Packing and covering with congruent convex disks
* Extremal graph and hypergraph theory
* Distribution of distances among finitely many points
* Epsilon-nets and Vapnik--Chervonenkis dimension
* Geometric graph theory
* Geometric discrepancy theory
* And much more

Table of contents

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  1. Part I: Arrangements of Convex Sets

  2. Part II: Arrangements of Points and Lines

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