Least action principle of crystal formation of dense packing type and Kepler's conjecture /
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...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; River Edge, NJ :
World Scientific,
2001.
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| Series: | Nankai tracts in mathematics ;
v. 3. |
| Subjects: | |
| Online Access: |
Full text (Emmanuel users only) |
Table of 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.