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#### Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture

World Scientific Publishing Company 2001; US$ 163.00The 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... more...

#### Finite Packing and Covering

Cambridge University Press 2004; US$ 108.00This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies. more...

#### The Pursuit of Perfect Packing

CRC Press 2000; US$ 44.95In 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, physics,... more...

#### Covering Codes

Elsevier Science 1997; US$ 260.00The 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... more...

#### Codes on Euclidean Spheres

Elsevier Science 2001; US$ 220.00Codes 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... more...

#### The Pursuit of Perfect Packing, Second Edition

CRC Press 2008; US$ 79.95Coauthored 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... more...

#### The Kepler Conjecture

Springer New York 2011; US$ 89.99The 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... more...

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