OFFSET
0,1
COMMENTS
Center density of densest packing of equal circles in two dimensions (achieved for example by the A2 lattice).
Let a equal the length of one side of an equilateral triangle and let b equal the radius of the circle inscribed in that triangle. This sequence gives the decimal expansion of b/a. - Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Feb 20 2004
The constant (3+sqrt 3)/6, which is 0.5 larger than this, plays a role in Borsuk's conjecture. - Arkadiusz Wesolowski, Mar 17 2014
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
N. J. A. Sloane and Andrey Zabolotskiy, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).
Wikipedia, Borsuk's conjecture
EXAMPLE
0.28867513459481288225457439025097872782380087563506343800930116324198883615...
MATHEMATICA
RealDigits[N[1/Sqrt[12], 200]] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
PROG
(PARI) 1/sqrt(12) \\ Charles R Greathouse IV, Oct 31 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved