Mathematics Department, Princeton University, Princeton, USA
Mathematical Science Department, AT&T Bell Laboratories, Murray Hill, USA
34k Accesses
1833 Citations
15 Altmetric
The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.
J. H. Conway
N. J. A. Sloane
This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format.
Book Title: Sphere Packings, Lattices and Groups
Authors: J. H. Conway, N. J. A. Sloane
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-1-4757-2016-7
Publisher: Springer New York, NY
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag New York 1988
eBook ISBN: 978-1-4757-2016-7Published: 17 April 2013
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XXVII, 665
Topics: Group Theory and Generalizations, Number Theory, Combinatorics, Theoretical, Mathematical and Computational Physics, Math. Applications in Chemistry, Computational Intelligence