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Combinatorial Geometry 1st Edition

ISBN-13: 978-0471588900
ISBN-10: 0471588903
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Editorial Reviews

From the Publisher

A broad perspective on an area of discrete mathematics, combinatorial geometry demonstrates that important results in many areas of number theory can be established by easy geometric arguments. This book is a comprehensive overview of the field. Includes numerous exercises and solutions.

From the Inside Flap

How many objects of a given shape and size can be packed into a large box of fixed volume? Can one plant n trees in an orchard, not all along the same line, so that every line determined by two trees will pass through a third? These questions, raised by Hilbert and Sylvester roughly one hundred years ago, have generated a lot of interest among professional and amateur mathematicians and scientists. They have led to the birth of a new mathematical discipline with close ties to classical geometry and number theory, and with many applications in coding theory, potential theory, computational geometry, computer graphics, robotics , etc. Combinatorial Geometry offers a self-contained introduction to this rapidly developing field, where combinatorial and probabilistic (counting) methods play a crucial role. This book has grown out of the material of both undergraduate and graduate courses in mathematics and computer science given by János Pach at the Courant Institute of Mathematical Sciences, New York University. Divided into two parts— Arrangements of Convex Sets and Arrangements of Points and Lines—it presents and explains some of the most important and ingenious results in combinatorial geometry, including:
  • Dowker’s theorems
  • Fáry’s theorem
  • Fejes Tóth’ stheorems
  • Methods of Blichtfeldt and Rogers
  • Minkowski—Hlawka theorem
  • Koebe’s representation theorem
  • Lipton—Tarjan separator theorem
  • Theorems of Erd???s, Turán, and Ramsey
  • Szemerédi’s regularity lemma
  • Szemerédi—Trotter theorems
  • Methods of Clarkson, Edelsbrunner, Guibas, Sharir, and Welzl
  • Counterexample to Borsuk’s conjecture
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