Introduction to Geometric Probability

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Overview

Elementary geometry in n-dimensional Euclidean space is a subject that, under the stimulus of computational geometry, is regaining its former position. This is the first textbook that addresses some fundamental problems of Euclidean geometry that have been solved over the last half-century. The authors, who have made significant contributions to the subject, have taken pains to keep the exposition elementary, making the relationship between it and combinatorics transparent. It should be required reading of anyone in mathematics or computer science who deals with the visual display of information.
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Editorial Reviews

From the Publisher
"Elementary methods and exceptionally clear exposition bring a once seemingly advanced subject within the ken of a wide audience of mathematics students. Highly recommended for upper-division undergraduate and graduate students." Choice

"The exposition is marvellous: clear and precise... The powerful theory of valuations, intrinsic volumes and invariant measures built by Hadwiger, Groemer, McMullen and others is an impressive development. The beautiful exposition would make this volume worthwhile even if Klain and Rota hadn't 'something new' to say." Bulletin of the AMS

"The text is very elegant...This book is a very tantalizing one in that there is a definite sense that much of the subject is mature, even the combinatorial analogies." Mathematical Reviews

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Product Details

  • ISBN-13: 9780521596541
  • Publisher: Cambridge University Press
  • Publication date: 2/28/2006
  • Series: Lezioni Lincee Series
  • Edition description: New Edition
  • Pages: 196
  • Product dimensions: 5.43 (w) x 8.50 (h) x 0.43 (d)

Table of Contents

Preface
Using this book
1 The Buffon needle problem 1
2 Valuation and integral 6
3 A discrete lattice 13
4 The intrinsic volumes for parallelotopes 30
5 The lattice of polyconvex sets 42
6 Invariant measures on Grassmannians 60
7 The intrinsic volumes for polyconvex sets 86
8 A characterization theorem for volume 98
9 Hadwiger's characterization theorem 118
10 Kinematic formulas for polyconvex sets 146
11 Polyconvex sets in the sphere 154
Bibliography 168
Index of symbols 174
Index 176
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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted May 5, 2004

    Brilliant Explanation

    Wonderful description of complex material in a way that makes it accessible to any student of mathematics.

    Was this review helpful? Yes  No   Report this review
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