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Sphere Packings

  • Textbook
  • © 1999

Overview

Authors:
  1. Chuanming Zong

    1. Institute of Mathernatics Chinese Academy of Sciences, PR China

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Editors:
  1. John Talbot

    1. Department of Mathematics, University College London, London, UK

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Part of the book series: Universitext (UTX)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Gregory-Newton Problem and Kepler’s Conjecture

    Pages 1-21

  3. Positive Definite Quadratic Forms and Lattice Sphere Packings

    Pages 23-45

  4. Lower Bounds for the Packing Densities of Spheres

    Pages 47-63

  5. Lower Bounds for the Blocking Numbers and the Kissing Numbers of Spheres

    Pages 65-77

  6. Sphere Packings Constructed from Codes

    Pages 79-89

  7. Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres I

    Pages 91-102

  8. Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres II

    Pages 103-123

  9. Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres III

    Pages 125-137

  10. The Kissing Numbers of Spheres in Eight and Twenty-Four Dimensions

    Pages 139-151

  11. Multiple Sphere Packings

    Pages 153-163

  12. Holes in Sphere Packings

    Pages 165-182

  13. Problems of Blocking Light Rays

    Pages 183-198

  14. Finite Sphere Packings

    Pages 199-217

  15. Back Matter

    Pages 219-242
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Keywords

About this book

Sphere Packings is one of the most attractive and challenging subjects in mathematics. Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with othe subjects found. Thus, though some of its original problems are still open, sphere packings has been developed into an important discipline. This book tries to give a full account of this fascinating subject, especially its local aspects, discrete aspects and its proof methods.

Reviews

From the reviews:

"Problems dealing with sphere packings have attracted the interest of mathematicians for more than three centuries. Important contributions are due to Kepler, Newton and Gregory, Lagrange, Seeber and Gauss, Dirichlet, Hermite, Korkine and Zolotarev, Minkowski, Thue, Vorono\u\i, Blichfeldt, Delone, Davenport, van der Waerden and many living mathematicians. One reason for this interest is the fact that there are many completely different aspects of sphere packings. These include the following: dense lattice and non-lattice packing of spheres in low and in general dimensions, multiple packings, geometric theory of positive definite quadratic forms and reduction theory, reduction theory of lattices and their computational aspects, special lattices such as the Leech lattice and relations to coding, information and group theory, finite packings of spheres, problems dealing with kissing and blocking numbers and other problems of discrete geometry. There is a series of books in which some of these aspects are dealt with thoroughly,...

The merit of Zong's book is that it covers all of the above aspects in a concise, elegant and readable form and thus gives the reader a good view of the whole area. Several of the most recent developments are also included."  (Peter M. Gruber, Mathematical Reviews) 

Authors, Editors and Affiliations

  • Department of Mathematics, University College London, London, UK

    John Talbot

  • Institute of Mathernatics Chinese Academy of Sciences, PR China

    Chuanming Zong

Bibliographic Information

  • Book Title: Sphere Packings

  • Authors: Chuanming Zong

  • Editors: John Talbot

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/b98975

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98794-1Published: 19 August 1999

  • Softcover ISBN: 978-1-4757-8148-9Published: 08 April 2013

  • eBook ISBN: 978-0-387-22780-1Published: 20 January 2008

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 242

  • Topics: Combinatorics, Number Theory

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