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Author | : J.H. Conway |
Publisher | : Springer Science & Business Media |
Total Pages | : 724 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475722494 |
Download Sphere Packings, Lattices and Groups Book in PDF, ePub and Kindle
The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.
Author | : Samuel L. P. Ferguson |
Publisher | : |
Total Pages | : 208 |
Release | : 1997 |
Genre | : Sphere packings |
ISBN | : |
Download Sphere Packings, V. Book in PDF, ePub and Kindle
Author | : Chuanming Zong |
Publisher | : Springer Science & Business Media |
Total Pages | : 245 |
Release | : 2008-01-20 |
Genre | : Mathematics |
ISBN | : 0387227806 |
Download Sphere Packings Book in PDF, ePub and Kindle
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.
Author | : Thomas Callister Hales |
Publisher | : Cambridge University Press |
Total Pages | : 286 |
Release | : 2012-09-06 |
Genre | : Mathematics |
ISBN | : 0521617707 |
Download Dense Sphere Packings Book in PDF, ePub and Kindle
The definitive account of the recent computer solution of the oldest problem in discrete geometry.
Author | : John Conway |
Publisher | : Springer Science & Business Media |
Total Pages | : 778 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475765681 |
Download Sphere Packings, Lattices and Groups Book in PDF, ePub and Kindle
The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.
Author | : John H. Conway |
Publisher | : Springer Science & Business Media |
Total Pages | : 690 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475720165 |
Download Sphere Packings, Lattices and Groups Book in PDF, ePub and Kindle
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.
Author | : Thomas M. Thompson |
Publisher | : |
Total Pages | : 252 |
Release | : 1983 |
Genre | : Error-correcting codes (Information theory) |
ISBN | : 9780883850008 |
Download From Error-correcting Codes Through Sphere Packings to Simple Groups Book in PDF, ePub and Kindle
Author | : Jeffrey C. Lagarias |
Publisher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2011-11-09 |
Genre | : Mathematics |
ISBN | : 1461411297 |
Download The Kepler Conjecture Book in PDF, ePub and Kindle
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.
Author | : Denis Weaire |
Publisher | : CRC Press |
Total Pages | : 147 |
Release | : 2000-01-01 |
Genre | : Mathematics |
ISBN | : 142003331X |
Download The Pursuit of Perfect Packing Book in PDF, ePub and Kindle
In 1998 Thomas Hales dramatically announced the solution of a problem that has long teased eminent mathematicians: what is the densest possible arrangement of identical spheres? The Pursuit of Perfect Packing recounts the story of this problem and many others that have to do with packing things together. The examples are taken from mathematics, phy
Author | : Károly Bezdek |
Publisher | : Springer Science & Business Media |
Total Pages | : 186 |
Release | : 2013-08-04 |
Genre | : Mathematics |
ISBN | : 146148118X |
Download Lectures on Sphere Arrangements – the Discrete Geometric Side Book in PDF, ePub and Kindle
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.