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Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture
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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/√18. In 1611, Johannes Kepler had already "conjectured" that p/√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 p/√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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Readership: Researchers in classical geometry and solid state physics.
World Scientific; January 2001
425 pages; ISBN 9789812384911
Read online, or download in secure PDF format
425 pages; ISBN 9789812384911
Read online, or download in secure PDF format
Subject categories
- Academic > Mathematics > Algebra > Graph theory
- Academic > Mathematics > Algebra > Combinatorial packing and covering
- Academic > Mathematics > General > Vinogradov, Ivan Matveevich, 1891-
- Academic > Mathematics > General > Mathematics; Periodicals
- Academic > Mathematics > General > Mathematics; Study and teaching
- Mathematics > Geometry
- Science > Solid State Physics
ISBNs
9789810246709
9789812384911
981238491X