## Hermite Constants

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

The Hermite constant is defined for Dimension as the value

(Le Lionnais 1983). In other words, they are given by

where is the maximum lattice Packing Density for Hypersphere Packing and is the Content of the -Hypersphere. The first few values of are 1, 4/3, 2, 4, 8, 64/3, 64, 256, .... Values for larger are not known.

For sufficiently large ,

See also Hypersphere Packing, Kissing Number, Sphere Packing

References

Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hermit/hermit.html

Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, p. 20, 1993.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 38, 1983.

© 1996-9 Eric W. Weisstein
1999-05-25