Dense Sphere Packings

Author : Thomas Callister Hales
Publisher : Cambridge University Press
ISBN 13 : 0521617707
Total Pages : 286 pages
Book Rating : 4.03/5 ( download)

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Download or read book Dense Sphere Packings written by Thomas Callister Hales and published by Cambridge University Press. This book was released on 2012-09-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive account of the recent computer solution of the oldest problem in discrete geometry.

Author : Thomas Hales
Publisher : Cambridge University Press
ISBN 13 : 113957647X
Total Pages : 286 pages
Book Rating : 4.75/5 ( download)

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Download or read book Dense Sphere Packings written by Thomas Hales and published by Cambridge University Press. This book was released on 2012-09-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.

Author : J.H. Conway
Publisher : Springer Science & Business Media
ISBN 13 : 1475722494
Total Pages : 724 pages
Book Rating : 4.99/5 ( download)

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Download or read book Sphere Packings, Lattices and Groups written by J.H. Conway and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Chuanming Zong
Publisher : Springer Science & Business Media
ISBN 13 : 0387227806
Total Pages : 242 pages
Book Rating : 4.01/5 ( download)

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Download or read book Sphere Packings written by Chuanming Zong and published by Springer Science & Business Media. This book was released on 2008-01-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jeffrey C. Lagarias
Publisher : Springer Science & Business Media
ISBN 13 : 1461411297
Total Pages : 456 pages
Book Rating : 4.91/5 ( download)

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Download or read book The Kepler Conjecture written by Jeffrey C. Lagarias and published by Springer Science & Business Media. This book was released on 2011-11-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Thomas Callister Hales
Publisher :
ISBN 13 : 9781139568708
Total Pages : 287 pages
Book Rating : 4.01/5 ( download)

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Download or read book Dense Sphere Packings written by Thomas Callister Hales and published by . This book was released on 2014-05-14 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive account of the recent computer solution of the oldest problem in discrete geometry.

Author : Denis Weaire
Publisher : CRC Press
ISBN 13 : 142003331X
Total Pages : 147 pages
Book Rating : 4.11/5 ( download)

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Download or read book The Pursuit of Perfect Packing written by Denis Weaire and published by CRC Press. This book was released on 2000-01-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Chuanming Zong
Publisher : Springer Science & Business Media
ISBN 13 : 0387987940
Total Pages : 245 pages
Book Rating : 4.41/5 ( download)

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Download or read book Sphere Packings written by Chuanming Zong and published by Springer Science & Business Media. This book was released on 1999-08-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jacques Martinet
Publisher : Springer Science & Business Media
ISBN 13 : 3662051672
Total Pages : 535 pages
Book Rating : 4.72/5 ( download)

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Download or read book Perfect Lattices in Euclidean Spaces written by Jacques Martinet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.

Author : Thomas M. Thompson
Publisher :
ISBN 13 : 9780883850008
Total Pages : 252 pages
Book Rating : 4.01/5 ( download)

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Download or read book From Error-correcting Codes Through Sphere Packings to Simple Groups written by Thomas M. Thompson and published by . This book was released on 1983 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: