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...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
2001.
|
| Schriftenreihe: | Nankai tracts in mathematics ;
v. 3. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 online resource (xxi, 402 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 397-399) and index. |
| ISBN: | 981238491X 9789812384911 9810246706 9789810246709 |
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| 504 | |a Includes bibliographical references (pages 397-399) and index. | ||
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| 505 | 0 | |a 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. | |
| 520 | |a 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 | ||
| 650 | 0 | |a Kepler's conjecture. |0 http://id.loc.gov/authorities/subjects/sh2001008320 | |
| 650 | 0 | |a Sphere packings. |0 http://id.loc.gov/authorities/subjects/sh2001008315 | |
| 650 | 0 | |a Crystallography, Mathematical. |0 http://id.loc.gov/authorities/subjects/sh85034501 | |
| 650 | 6 | |a Conjecture de Kepler. | |
| 650 | 6 | |a Empilements de sphères. | |
| 650 | 6 | |a Cristallographie mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Combinatorics. |2 bisacsh | |
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| author | Hsiang, Wu Yi, 1937- |
| author_GND | http://id.loc.gov/authorities/names/n80137813 |
| author_facet | Hsiang, Wu Yi, 1937- |
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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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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:25Z |
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| spelling | Hsiang, Wu Yi, 1937- https://id.oclc.org/worldcat/entity/E39PBJwHhQrVXp9FB3JMfQBHG3 http://id.loc.gov/authorities/names/n80137813 Least action principle of crystal formation of dense packing type and Kepler's conjecture / Wu-Yi Hsiang. Singapore ; River Edge, NJ : World Scientific, 2001. 1 online resource (xxi, 402 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Nankai tracts in mathematics ; v. 3 Includes bibliographical references (pages 397-399) and index. Print version record. 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. 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 Kepler's conjecture. http://id.loc.gov/authorities/subjects/sh2001008320 Sphere packings. http://id.loc.gov/authorities/subjects/sh2001008315 Crystallography, Mathematical. http://id.loc.gov/authorities/subjects/sh85034501 Conjecture de Kepler. Empilements de sphères. Cristallographie mathématique. MATHEMATICS Combinatorics. bisacsh Crystallography, Mathematical fast Kepler's conjecture fast Sphere packings fast has work: Least action principle of crystal formation of dense packing type and Kepler's conjecture (Text) https://id.oclc.org/worldcat/entity/E39PCFtHTBvf73Tdyt4ydTGXgq https://id.oclc.org/worldcat/ontology/hasWork 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 Nankai tracts in mathematics ; v. 3. http://id.loc.gov/authorities/names/n2001000055 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=83665 Volltext |
| spellingShingle | Hsiang, Wu Yi, 1937- Least action principle of crystal formation of dense packing type and Kepler's conjecture / Nankai tracts in mathematics ; 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. Kepler's conjecture. http://id.loc.gov/authorities/subjects/sh2001008320 Sphere packings. http://id.loc.gov/authorities/subjects/sh2001008315 Crystallography, Mathematical. http://id.loc.gov/authorities/subjects/sh85034501 Conjecture de Kepler. Empilements de sphères. Cristallographie mathématique. MATHEMATICS Combinatorics. bisacsh Crystallography, Mathematical fast Kepler's conjecture fast Sphere packings fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2001008320 http://id.loc.gov/authorities/subjects/sh2001008315 http://id.loc.gov/authorities/subjects/sh85034501 |
| title | Least action principle of crystal formation of dense packing type and Kepler's conjecture / |
| title_auth | Least action principle of crystal formation of dense packing type and Kepler's conjecture / |
| title_exact_search | Least action principle of crystal formation of dense packing type and Kepler's conjecture / |
| title_full | Least action principle of crystal formation of dense packing type and Kepler's conjecture / Wu-Yi Hsiang. |
| title_fullStr | Least action principle of crystal formation of dense packing type and Kepler's conjecture / Wu-Yi Hsiang. |
| title_full_unstemmed | Least action principle of crystal formation of dense packing type and Kepler's conjecture / Wu-Yi Hsiang. |
| title_short | Least action principle of crystal formation of dense packing type and Kepler's conjecture / |
| title_sort | least action principle of crystal formation of dense packing type and kepler s conjecture |
| topic | Kepler's conjecture. http://id.loc.gov/authorities/subjects/sh2001008320 Sphere packings. http://id.loc.gov/authorities/subjects/sh2001008315 Crystallography, Mathematical. http://id.loc.gov/authorities/subjects/sh85034501 Conjecture de Kepler. Empilements de sphères. Cristallographie mathématique. MATHEMATICS Combinatorics. bisacsh Crystallography, Mathematical fast Kepler's conjecture fast Sphere packings fast |
| topic_facet | Kepler's conjecture. Sphere packings. Crystallography, Mathematical. Conjecture de Kepler. Empilements de sphères. Cristallographie mathématique. MATHEMATICS Combinatorics. Crystallography, Mathematical Kepler's conjecture Sphere packings |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=83665 |
| work_keys_str_mv | AT hsiangwuyi leastactionprincipleofcrystalformationofdensepackingtypeandkeplersconjecture |