Least action principle of crystal formation of dense packing type and the proof of Kepler's conjecture / Hsiang, Wu-Yi.

Format:

Book

Author/Creator:

Hsiang, Wu Yi, 1937-

Series:

Nankai tracts in mathematics

Language:

English

Subjects (All):

Kepler's conjecture.

Sphere packings.

Crystallography, Mathematical.

Physical Description:

1 online resource (425 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, 2001.

Language Note:

English

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611869700

9781281869708

1281869708

9789812384911

981238491X

OCLC:

475900343