ENGLISH

Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture

Book information

Publisher
World Scientific Pub Co Inc
Year
2001
ISBN
9810246706, 9789810246709
Language
english
Format
DJVU
Filesize
2 MB (2221175 bytes)
Edition
1
Pages
300\425
DPI
300
Time added
2024-07-31 12:46:10

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 B/√18. In 1611, Johannes Kepler had already "conjectured" that B/√18 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 B/√18 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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