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Sphere Packings
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Book Synopsis Sphere Packings, Lattices and Groups by : J.H. Conway
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.
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 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.
Book Synopsis Dense Sphere Packings by : Thomas Callister Hales
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.
Book Synopsis Sphere Packings, Lattices and Groups by : John Conway
Download or read book Sphere Packings, Lattices and Groups written by John Conway and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sphere Packings, Lattices and Groups by : John H. Conway
Download or read book Sphere Packings, Lattices and Groups written by John H. Conway and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Error-Correcting Codes Through Sphere Packings to Simple Groups by : Thomas M. Thompson
Download or read book From Error-Correcting Codes Through Sphere Packings to Simple Groups written by Thomas M. Thompson and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels lead to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighboring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the "Enormous Theorem"—the classification of all simple groups whose entire proof runs some 10,000+ pages—and these connections, along with the fascinating history and the proof of the simplicity of one of those "sporatic" simple groups, are presented at an undergraduate mathematical level.
Book Synopsis From Error-correcting Codes Through Sphere Packings to Simple Groups by : Thomas M. Thompson
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:
Book Synopsis Introduction to Circle Packing by : Kenneth Stephenson
Download or read book Introduction to Circle Packing written by Kenneth Stephenson and published by Cambridge University Press. This book was released on 2005-04-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Book Synopsis International Tables for Crystallography,Volume C by : E. Prince
Download or read book International Tables for Crystallography,Volume C written by E. Prince and published by Springer Science & Business Media. This book was released on 2004-01-31 with total page 1033 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Tables for Crystallography are no longer available for purchase from Springer. For further information please contact Wiley Inc. (follow the link on the right hand side of this page). The purpose of Volume C is to provide the mathematical, physical and chemical information needed for experimental studies in structural crystallography. The volume covers all aspects of experimental techniques, using all three principal radiation types, from the selection and mounting of crystals and production of radiation, through data collection and analysis, to interpretation of results. As such, it is an essential source of information for all workers using crystallographic techniques in physics, chemistry, metallurgy, earth sciences and molecular biology.
Book Synopsis Inorganic Structural Chemistry by : Ulrich M]ller
Download or read book Inorganic Structural Chemistry written by Ulrich M]ller and published by John Wiley & Sons. This book was released on 1993-04-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the structural principles of inorganic-chemical molecules and solids. Traditional concepts and modern approaches are considered and demonstrated with the aid of examples. The most important structural types are examined from different perspectives.
Book Synopsis Chemical Topology by : Danail Bonchev
Download or read book Chemical Topology written by Danail Bonchev and published by CRC Press. This book was released on 2000-07-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology has been extensively applied in the study of chemically linked and knotted structures, and also in the study of many biologically significant molecules such as proteins and DNA. These are the themes that are addressed in this volume of the Mathematical Chemistry series. The topological chirality of knotted and linked molecular species and the invariants that may characterize them are explored in detail.
Book Synopsis Sphere Packings, V. by : Samuel L. P. Ferguson
Download or read book Sphere Packings, V. written by Samuel L. P. Ferguson and published by . This book was released on 1997 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1964 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Pursuit of Perfect Packing by : Denis Weaire
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
Book Synopsis Colloid Science by : Douglas H. Everett
Download or read book Colloid Science written by Douglas H. Everett and published by Royal Society of Chemistry. This book was released on 1990-05-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialist Periodical Reports provide systematic and detailed review coverage of progress in the major areas of chemical research. Written by experts in their specialist fields the series creates a unique service for the active research chemist, supplying regular critical in-depth accounts of progress in particular areas of chemistry. For over 80 years the Royal Society of Chemistry and its predecessor, the Chemical Society, have been publishing reports charting developments in chemistry, which originally took the form of Annual Reports. However, by 1967 the whole spectrum of chemistry could no longer be contained within one volume and the series Specialist Periodical Reports was born. The Annual Reports themselves still existed but were divided into two, and subsequently three, volumes covering Inorganic, Organic and Physical Chemistry. For more general coverage of the highlights in chemistry they remain a 'must'. Since that time the SPR series has altered according to the fluctuating degree of activity in various fields of chemistry. Some titles have remained unchanged, while others have altered their emphasis along with their titles; some have been combined under a new name whereas others have had to be discontinued.
Book Synopsis Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture by : Wu Yi Hsiang
Download or read book Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture written by Wu Yi Hsiang and published by World Scientific. This book was released on 2001 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal known density of p/OeU18. In 1611, Johannes Kepler had already conjectured that p/OeU18 should be the optimal density of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler''s conjecture that p/OeU18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry."
Book Synopsis Lectures on Sphere Arrangements – the Discrete Geometric Side by : Károly Bezdek
Download or read book Lectures on Sphere Arrangements – the Discrete Geometric Side written by Károly Bezdek and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
