03191nam 2200649Ia 450 991045614970332120200520144314.01-281-86970-89786611869700981-238-491-X(CKB)111087028338014(EBL)183742(OCoLC)475900343(SSID)ssj0000190753(PQKBManifestationID)11156712(PQKBTitleCode)TC0000190753(PQKBWorkID)10180726(PQKB)11633254(MiAaPQ)EBC183742(WSP)00004741(Au-PeEL)EBL183742(CaPaEBR)ebr10255610(CaONFJC)MIL186970(EXLCZ)9911108702833801420010713d2001 uy 0engur|n|---|||||txtccrLeast action principle of crystal formation of dense packing type and the proof of Kepler's conjecture[electronic resource] /Hsiang, Wu-YiSingapore ;River Edge, NJ World Scientific20011 online resource (425 p.)Nankai tracts in mathematicsDescription based upon print version of record.981-02-4670-6 Includes bibliographical references.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; IndexThe 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 ofNankai tracts in mathematicsKepler's conjectureSphere packingsCrystallography, MathematicalElectronic books.Kepler's conjecture.Sphere packings.Crystallography, Mathematical.511/.6516Hsiang Wu Yi1937-47829MiAaPQMiAaPQMiAaPQBOOK9910456149703321Least action principle of crystal formation of dense packing type and the proof of Kepler's conjecture2283427UNINA