By Wu Yi Hsiang
The dense packing of microscopic spheres (atoms) is the fundamental geometric association in crystals of mono-atomic components with vulnerable covalent bonds, which achieves the optimum "known density" of B/O18. In 1611, Johannes Kepler had already "conjectured" that B/O18 might be the optimum "density" of sphere packings. hence, the crucial difficulties within the research 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 end result of optimization of density. This ebook presents a self-contained evidence of either, utilizing vector algebra and round geometry because the major ideas and within the culture of classical geometry.