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010   $a1-281-86970-8
010   $a9786611869700
010   $a981-238-491-X
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035   $a(EBL)183742
035   $a(OCoLC)475900343
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035   $a(PQKBTitleCode)TC0000190753
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100   $a20010713d2001      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aLeast action principle of crystal formation of dense packing type and the proof of Kepler's conjecture$b[electronic resource] /$fHsiang, Wu-Yi
210   $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$d2001
215   $a1 online resource (425 p.)
225 1 $aNankai tracts in mathematics
300   $aDescription based upon print version of record.
311   $a981-02-4670-6 
320   $aIncludes bibliographical references.
327   $aContents; 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
330   $aThe dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal ""known density"" of p/v18. In 1611, Johannes Kepler had already ""conjectured"" that p/v18 should be the optimal ""density"" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/v18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of
410  0$aNankai tracts in mathematics
606   $aKepler's conjecture
606   $aSphere packings
606   $aCrystallography, Mathematical
608   $aElectronic books.
615  0$aKepler's conjecture.
615  0$aSphere packings.
615  0$aCrystallography, Mathematical.
676   $a511/.6
676   $a516
700   $aHsiang$b Wu Yi$f1937-$047829
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910456149703321
996   $aLeast action principle of crystal formation of dense packing type and the proof of Kepler's conjecture$92283427
997   $aUNINA