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An extreme covering of 4-space by spheres

Published online by Cambridge University Press:  09 April 2009

T. J. Dickson
T. J. Dickson
Affiliation:
South Australian Institute of Technology and University of Adelaide
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Let Λ be a lattice in n-dimensional Euclidean space En. For any lattice there is a unique minimal positive number μ such that if spheres of radius μ are placed at the points of the lattice then the entire space is covered, i.e. every point in En lies in at least one of the spheres. The density of this covering is defined to be θn(Λ) = Jnμn/d(Λ), where Jn is the volume of an n-dimensional unit sphere and d(Λ) is the determinant of the lattice.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 2 , May 1966 , pp. 179 - 192
Copyright
Copyright © Australian Mathematical Society 1966

References

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