Least action principle of crystal formation of dense packing type and Kepler's conjecture
- 作者: Hsiang, Wu Yi,
- 出版: Singapore ;River Edge, NJ : World Scientific 2001.
- 稽核項: 1 online resource (xxi, 402 pages) :illustrations.
- 叢書名: Nankai tracts in mathematics ;v. 3
- 標題: Crystallography, Mathematical. , MATHEMATICS Combinatorics. , Cristallographie mathématique. , Combinatorics. , Sphere packings. , Empilements de sphères. , Kepler's conjecture. , Electronic books. , MATHEMATICS , Conjecture de Kepler.
- ISBN: 9810246706 , 9789810246709
- 試查全文@TNUA:
- 附註: Includes bibliographical references (pages 397-399) and index. 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.
- 摘要: 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.
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- 系統號: 005302150
- 資料類型: 電子書
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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 B/û18. In 1611, Johannes Kepler had already ?conjectured? that B/û18 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 B/û18 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 and in the tradition of classical geometry.
來源: Google Book
來源: Google Book
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