Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture

Released on by Wu Yi Hsiang
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  • Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture Book Detail

  • Author : Wu Yi Hsiang
  • Release Date : 2001
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 444
  • ISBN 13 : 9789812384911
  • File Size : 75,75 MB
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Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture by Wu Yi Hsiang PDF Summary

Book Description: 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/OeU18. In 1611, Johannes Kepler had already conjectured that p/OeU18 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/OeU18 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 density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry."

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The Kepler Conjecture

The Kepler Conjecture

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The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem