Download E-books Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture PDF

By Wu Yi Hsiang

The dense packing of microscopic spheres (atoms) is the fundamental geometric association in crystals of mono-atomic parts with vulnerable covalent bonds, which achieves the optimum "known density" of B/O18. In 1611, Johannes Kepler had already "conjectured" that B/O18 will be the optimum "density" of sphere packings. hence, the principal difficulties within the examine of sphere packings are the facts of Kepler's conjecture that B/O18 is the optimum density, and the constructing of the least motion precept that the hexagonal dense packings in crystals are the geometric outcome of optimization of density. This publication offers a self-contained evidence of either, utilizing vector algebra and round geometry because the major concepts and within the culture of classical geometry.

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