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The Covering Of Space By Spheres

Published online by Cambridge University Press:  20 November 2018

E. S. Barnes
E. S. Barnes*
Affiliation:
University of Sydney
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Bambah (1) has recently determined the most economical covering of three dimensional space by equal spheres whose centres form a lattice, the density of this covering being

1.1.

As is well known, this problem may be interpreted in terms of the inhomogeneous minimum of a positive definite quadratic form.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 293 - 304
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Bambah, R. P., On lattice coverings by spheres. Proc. Nat. Inst. Sci. India, 20 (1954), 25–52.Google Scholar
2. Hlawka, E., Ausfüllung und Überdeckung konvexer Körper durch konvexe Körper, Monatsh. Math. Phys., 53 (1949), 81–131.Google Scholar
3. Voronoï, G., Sur quelques propriétés des formes quadratiques positives parfaites, J. reine angew. Math. 133 (1907), 97–178.Google Scholar
4. Voronoï, G., Recherches sur les paralléloèdres primitifs (Part 1), ibid., 134 (1908), 198–287.Google Scholar
5. Voronoï, G., (Part 2), ibid., 136 (1909), 67–181.Google Scholar