Click Here to Download: https://ouo.io/uBKSxJ Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture By: Hsiang Wu-yi Publisher: World Scientific Print ISBN: 9789810246709, 9810246706 eText ISBN: 9789812384911, 981238491X Format: PDF Available from $ 188.00 USD SKU 9789812384911 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.
