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Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjectureby W Y Hsiang
World Scientific 2001; US$ 88.40The 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/√18. In 1611, Johannes Kepler had already "conjectured" that p/√18 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/√18 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... more...
The Pursuit of Perfect Packingby Tomaso Aste
CRC Press 2000; US$ 42.95In 1998 Thomas Hales dramatically announced the solution to the problem which has long teased eminent mathematicians: what is the densest possible arrangement of identical spheres? This text recounts the story of this problem and many others which have to do with packing things together. more...
Finite Packing and Coveringby Károly Jr Böröczky; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2004; US$ 95.00This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments and provides a comprehensive treatment of problems whose interplay was not clearly understood before. Two-dimensional and higher-dimensional arrangements are discussed separately, arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered. more...
Covering Codesby G. Cohen; I. Honkala; S. Litsyn; A. Lobstein
Elsevier 2005; US$ 179.00The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer. A number of unsolved problems suitable for research projects are also discussed. more...
Codes on Euclidean Spheresby T. Ericson; V. Zinoviev
Elsevier 2001; US$ 165.00Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results... more...
The Pursuit of Perfect Packingby Tomaso Aste
Taylor & Francis 2008; US$ 59.95Coauthored by one of the creators of the most efficient space packing solution, the Weaire???Phelan structure, The Pursuit of Perfect Packing, Second Edition explores a problem of importance in physics, mathematics, chemistry, biology, and engineering: the packing of structures. Maintaining its mathematical core, this edition continues and revises some of the stories from its predecessor while adding several new examples and applications. The book focuses on both scientific and everyday problems ranging from atoms to honeycombs. It describes packing models, such as the Kepler conjecture, Vorono?? decomposition, and Delaunay decomposition, as well as actual structure models, such as the Kelvin cell and the Weaire???Phelan structure. The authors... more...
The Kepler Conjectureby Jeffrey C. Lagarias
Springer 2011; US$ 74.95The 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... more...
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