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Covering a sphere with spheres

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers
C. A. Rogers
Affiliation:
University College, London
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We work throughout in n-dimensional Euclidean space. It has been clear, since the publication of [1], that it should be possible to obtain quite good upper bounds for the number of spherical caps of chord 2 required to cover the surface of a sphere of radius R > 1, and for the number of spheres of radius 1 required to cover a sphere of radius R > 1. But it is not quite simple to organize the necessary calculations to give estimates which are manageable, and which are as good as the method allows for all R > 1. The following results seem to be a reasonable compromise between precision and simplicity; but, for reasons we will give later, they are not completely satisfactory.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 2 , December 1963 , pp. 157 - 164
Copyright
Copyright © University College London 1963

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References

1.Rogers, C. A., “A note on coverings”, Mathematika, 4 (1957), 1–6.CrossRefGoogle Scholar