Abstract
Suppose that U is an open set in Euclidean N-space which has a finite volume |U|. A complete packing of U is a sequence of disjoint N-spheres C = {Sn} which are contained in U and whose total volume equals that of U. In an osculatory packing, the spheres are chosen recursively so that for all n larger than a certain value m, Sn has the largest radius of all spheres contained in U\(S1 ∪ … ∪ Sn-1) (S is the closure of S). An osculatory packing is simple if m = 1. If rn denotes the radius of Sn, the exponent of the packing is defined by: This quantity is of considerable interest since it measures the effectiveness of the packing of U by C.

This publication has 1 reference indexed in Scilit:

  • Convexity
    Published by Cambridge University Press (CUP) ,1958