Description |
1 online resource (xxi, 402 pages) : illustrations. |
Physical Medium |
polychrome |
Description |
text file |
Series |
Nankai tracts in mathematics ; v. 3
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Nankai tracts in mathematics ; v. 3.
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Bibliography |
Includes bibliographical references (pages 397-399) and index. |
Contents |
Foreword; Acknowledgment; List of Symbols; Chapter 1 Introduction; Chapter 2 The Basics of Euclidean and Spherical Geometries and a New Proof of the Problem of Thirteen Spheres; Chapter 3 Circle Packings and Sphere Packings; Chapter 4 Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells; Chapter 5 Estimates of Total Buckling Height; Chapter 6 The Proof of the Dodecahedron Conjecture; Chapter 7 Geometry of Type I Configurations and Local Extensions; Chapter 8 The Proof of Main Theorem I; Chapter 9 Retrospects and Prospects; References; Index. |
Summary |
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/v18. In 1611, Johannes Kepler had already "conjectured" that p/v18 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/v18 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 densi. |
Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
Subject |
Kepler's conjecture.
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Kepler's conjecture. |
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Sphere packings.
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Sphere packings. |
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Crystallography, Mathematical.
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Crystallography, Mathematical. |
Genre/Form |
Electronic books.
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Other Form: |
Print version: Hsiang, Wu Yi, 1937- Least action principle of crystal formation of dense packing type and Kepler's conjecture. Singapore ; River Edge, NJ : World Scientific, 2001 9810246706 (DLC) 2001045504 (OCoLC)47623942 |
ISBN |
981238491X (electronic book) |
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9789812384911 (electronic book) |
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