Closest Packing of Equal Spheres and Related Problems

Résumé du livre

The two-dimensional packing problem is discussed, using the concept of the lattice, and the lattice which determines the closest packing of equal circles is presented. Also, closest packing in terms of density is discussed and the density value for the closest regular packing is derived. The idea of sphere-clouds is introduced and used as an introduction to the closest packing of spheres. Lattice-like arrangements of spheres are considered, and the density of such a packing is determined. Two proofs, one by John Leech and one by A.H. Boerdijk, are presented to show that it is impossible for thirteen spheres of equal radius to be in contact with a fourteenth sphere of the same radius. A second related problem is presented, which when generalize reduces to the problem of finding the number of figures with (N + 1) vertices in N-space, choosing the vertices from given sets of points on given lines passing through a common point, subject to the restriction that no N lines lie in the same (N -1)-space. A solution by the author is presented and compared with a published solution. (Author).