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Record Nr. |
UNINA9910456149703321 |
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Autore |
Hsiang Wu Yi <1937-> |
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Titolo |
Least action principle of crystal formation of dense packing type and the proof of Kepler's conjecture [[electronic resource] /] / Hsiang, Wu-Yi |
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Pubbl/distr/stampa |
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Singapore ; ; River Edge, NJ, : World Scientific, 2001 |
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ISBN |
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1-281-86970-8 |
9786611869700 |
981-238-491-X |
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Descrizione fisica |
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1 online resource (425 p.) |
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Collana |
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Nankai tracts in mathematics |
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Disciplina |
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Soggetti |
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Kepler's conjecture |
Sphere packings |
Crystallography, Mathematical |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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