Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T14:57:55.404Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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