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Extreme coverings of n-space by spheres

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes  and
T. J. Dickson
E. S. Barnes
Affiliation:
University of Adelaide, South Australia South Australian Institute of Technology
T. J. Dickson
Affiliation:
University of Adelaide, South Australia South Australian Institute of Technology
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It is well known that the problem of determining the most economical covering of n-dimensional Eucidean space, by equal spheres whose centres form a lattice, may be formulated in terms of positive definite quadratic forms, as follows: Let

be positive definite, and

For real α, set

(the minimum being taken over integral x),

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 115 - 127
Copyright
Copyright © Australian Mathematical Society 1967

References

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