Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T11:43:23.600Z Has data issue: false hasContentIssue false
  • English
  • Français

Covering space with equal spheres

Published online by Cambridge University Press:  26 February 2010

H. S. M. Coxeter ,
L. Few  and
C. A. Rogers
H. S. M. Coxeter
Affiliation:
The University of Toronto. University College, London.
L. Few
Affiliation:
The University of Toronto. University College, London.
C. A. Rogers
Affiliation:
The University of Toronto. University College, London.
Get access

Extract

In a recent paper Rogers [13] has discussed packings of equal spheres in n-dimensional space and has shown that the density of such a packing cannot exceed a certain ratio σn. In this paper, we discuss coverings of space with equal spheres and, by using a method which is in some respects dual to that used by Rogers, we show that the density of such a covering must always be at least

Type
Research Article
Information
Mathematika , Volume 6 , Issue 2 , December 1959 , pp. 147 - 157
Copyright
Copyright © University College London 1959

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bambah, R. P., Proc. Nat. Inst. Sci. India 20 (1954), 25–52.Google Scholar
2.Bambah, R. P., Proc. Camb. Phil. Soc., 50 (1954), 203–208.CrossRefGoogle Scholar
3.Barnes, E. S., Canadian J. of Math., 8 (1956), 293–304.CrossRefGoogle Scholar
4.Coxeter, H. S. M., Regular Polytopes (London, 1948).Google Scholar
5.Davenport, H. and Rogers, C. A., Duke Math. J., 14 (1947), 367–375.CrossRefGoogle Scholar
6.Dirchlet, G. L., J. reine angew. Math., 40 (1850), 216–219.Google Scholar
7.Erdös, P. and Rogers, C. A., Jour. London Math. Soc., 28 (1953), 287–293.CrossRefGoogle Scholar
8.Tóth, L. Fejes. Lagerungen in der Ebene, auf der Kugel und in Raum (Berlin, 1953).CrossRefGoogle Scholar
9.Few, L., Mathematika, 3 (1956), 136–139.CrossRefGoogle Scholar
10.Kershner, R., Amer. J. of Math., 61 (1939), 665–671.CrossRefGoogle Scholar
11.Rogers, C. A., Amer. J. of Math., 61 (1939), 665–671.Google Scholar
12.Rogers, C. A., Mathematika, 4 (1957), 1–6.CrossRefGoogle Scholar
13.Rogers, C. A., Proc. London Math. Soc. (3), 8 (1958), 609–620.CrossRefGoogle Scholar
14.Rogers, C. A., Mathematika, 6 (1959).CrossRefGoogle Scholar
15.Schläfli, L., Gesammelte math. Abhandlungen, I (Basel, 1950).CrossRefGoogle Scholar
16.Schläfli, L., GesammeUe math. Abhandlungen, II (Basel, 1953),CrossRefGoogle Scholar
17.Schmidt, Wolfgang, “Masstheorie in der Geometrie der Zahlen”, to appear in Acta Math.Google Scholar
18.Voronoï, G., J. reine angew. Math., 134 (1908), 198–287.CrossRefGoogle Scholar