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Combinatorial packing and covering

  • The Kepler Conjectureby

    Springer New York 2011; US$ 74.95

    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... more...

  • Finite Packing and Coveringby Károly Jr Böröczky

    Cambridge University Press 2004; US$ 108.00

    This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies. more...

  • Covering Codesby G. Cohen; I. Honkala; S. Litsyn; A. Lobstein

    Elsevier Science 1997; US$ 260.00

    The 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 Spheresby T. Ericson; V. Zinoviev

    Elsevier Science 2001; US$ 220.00

    Codes 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...

  • Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjectureby W Y Hsiang

    World Scientific Publishing Company 2001; US$ 163.00

    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/√18. In 1611, Johannes Kepler had already "conjectured" that p/√18 should be the optimal "density" of sphere packings. Thus, the central problems... more...

  • The Pursuit of Perfect Packing, Second Editionby Denis Weaire; Tomaso Aste

    CRC Press 2008; US$ 79.95

    Prefaces How Many Sweets in the Jar? Loose Change and Tight Packing A Teasing but Tractable Problem A Handful of Coins Order and Disorder Hard Problems with Hard Spheres The Greengrocer?s Dilemma Ordered Close Packing?The Kepler Problem The Kepler Conjecture Marvelous Clarity, Neurotic Anxiety: The Life of Kepler... more...

  • The Pursuit of Perfect Packingby Denis Weaire; Tomaso Aste

    CRC Press 2000; US$ 44.95

    How many sweets in the jar? Loose change and tight packing. Hard problems with hard spheres. Proof positive? Peas and pips. Enthusiastic admiration: the honeycomb. Toils and troubles with bubbles. The architecture of the world of atoms. Apollonius and concrete. The Giant's Causeway. Soccer balls, golfballs and buckyballs. Packings and kisses in high... more...

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