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On the Exponent of an Osculatory Packing

Published online by Cambridge University Press:  20 November 2018

David W. Boyd
David W. Boyd*
Affiliation:
California Institute of Technology, Pasadena, California
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 2 , April 1971 , pp. 355 - 363
Copyright
Copyright © Canadian Mathematical Society 1971

References

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