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Classical Topics in Discrete Geometry

  • Textbook
  • © 2010

Overview

Authors:
  1. Károly Bezdek

    1. Department of Mathematics & Statistics, University of Calgary, Calgary, Canada

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  • A valuable source of geometric problems
  • User-friendly exposition and up-to-date bibliography provide insight into the latest research
  • Useful as a textbook or a research monograph
  • Includes supplementary material: sn.pub/extras

Part of the book series: CMS Books in Mathematics (CMSBM)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Classical Topics Revisited

    1. Front Matter

      Pages 1-1
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    2. Sphere Packings

      • Károly Bezdek
      Pages 3-16

    3. Finite Packings by Translates of Convex Bodies

      • Károly Bezdek
      Pages 17-22

    4. Coverings by Homothetic Bodies - Illumination and Related Topics

      • Károly Bezdek
      Pages 23-33

    5. Coverings by Planks and Cylinders

      • Károly Bezdek
      Pages 35-45

    6. On the Volume of Finite Arrangements of Spheres

      • Károly Bezdek
      Pages 47-56

    7. Ball-Polyhedra as Intersections of Congruent Balls

      • Károly Bezdek
      Pages 57-68

  3. Selected Proofs

    1. Front Matter

      Pages 70-70
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    2. Selected Proofs on Sphere Packings

      • Károly Bezdek
      Pages 71-94

    3. Selected Proofs on Finite Packings of Translates of Convex Bodies

      • Károly Bezdek
      Pages 95-99

    4. Selected Proofs on Illumination and Related Topics

      • Károly Bezdek
      Pages 101-114

    5. Selected Proofs on Coverings by Planks and Cylinders

      • Károly Bezdek
      Pages 115-120

    6. Selected Proofs on the Kneser–Poulsen Conjecture

      • Károly Bezdek
      Pages 121-133

    7. Selected Proofs on Ball-Polyhedra

      • Károly Bezdek
      Pages 135-151

  4. Back Matter

    Pages 153-163
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Keywords

About this book

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.

Reviews

From the reviews:

“The present volume actually surveys packing and covering problems in Euclidean space and close cousins. … Bezdek … surveys the state of the art, best results, and outstanding conjectures for a host of problems. … Summing Up: Recommended. Academic audiences, upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 48 (5), January, 2011)

“The book is intended for graduate students interested in discrete geometry. The book provides a road map to the state-of-the-art of several topics in discrete geometry. It can also serve as a textbook for a graduate level course or a seminar. Additionally, the book is extremely current, with many references to as late as 2009–2010 publications.” (Alex Bogomolny, The Mathematical Association of America, August, 2010)

“This very interesting monograph contains a selection of topics in discrete geometry, mainly those on which the author and his collaborators have worked. … The many conjectures and problems to be found throughout the text will serve as an inspiration to many discrete geometers.” (Konrad Swanepoel, Zentralblatt MATH, Vol. 1207, 2011)

Authors and Affiliations

  • Department of Mathematics & Statistics, University of Calgary, Calgary, Canada

    Károly Bezdek

Bibliographic Information

  • Book Title: Classical Topics in Discrete Geometry

  • Authors: Károly Bezdek

  • Series Title: CMS Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-0600-7

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2010

  • Hardcover ISBN: 978-1-4419-0599-4Published: 07 July 2010

  • Softcover ISBN: 978-1-4614-2620-2Published: 05 September 2012

  • eBook ISBN: 978-1-4419-0600-7Published: 23 June 2010

  • Series ISSN: 1613-5237

  • Series E-ISSN: 2197-4152

  • Edition Number: 1

  • Number of Pages: XIV, 166

  • Topics: Geometry

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