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Combinatorial Geometry

Hardcover

£157.00

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Combinatorial Geometry

János Pach, Pankaj K. Agarwal

ISBN: 978-0-471-58890-0 November 1995 376 Pages

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Description

A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery 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
ARRANGEMENTS OF CONVEX SETS.

Geometry of Numbers.

Approximation of a Convex Set by Polygons.

Packing and Covering with Congruent Convex Discs.

Lattice Packing and Lattice Covering.

The Method of Cell Decomposition.

Methods of Blichfeldt and Rogers.

Efficient Random Arrangements.

Circle Packings and Planar Graphs.

ARRANGEMENTS OF POINTS AND LINES.

Extremal Graph Theory.

Repeated Distances in Space.

Arrangement of Lines.

Applications of the Bounds on Incidences.

More on Repeated Distances.

Geometric Graphs.

Epsilon Nets and Transversals of Hypergraphs.

Geometric Discrepancy.

Hints to Exercises.

Bibliography.

Indexes.