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Sphere Packings : Universitext - John Talbot

Sphere Packings


By: Chuanming Zong, John Talbot (Editor)


Published: 19th August 1999
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Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.

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, Voronoui, 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)

The Gregory-Newton Problem and Kepler's Conjecture
Positive Definite Quadratic Forms and Lattice Sphere Packings
Lower Bounds for the Packing Densities of Spheres
Lower Bounds for the Blocking Numbers and the Kissing Numbers of Spheres
Sphere Packings Constructed from Codes
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres I
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres II
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres III
The Kissing Numbers of Spheres in Eight and Twenty Four Dimensions
Multiple Sphere Packings
Holes in Sphere Packings
Problems of Blocking Light Rays
Finite Sphere Packings
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387987941
ISBN-10: 0387987940
Series: Universitext
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 242
Published: 19th August 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 15.24  x 1.91
Weight (kg): 0.54