

A020769


Decimal expansion of 1/sqrt(12) = 1/(2*sqrt(3)).


15



2, 8, 8, 6, 7, 5, 1, 3, 4, 5, 9, 4, 8, 1, 2, 8, 8, 2, 2, 5, 4, 5, 7, 4, 3, 9, 0, 2, 5, 0, 9, 7, 8, 7, 2, 7, 8, 2, 3, 8, 0, 0, 8, 7, 5, 6, 3, 5, 0, 6, 3, 4, 3, 8, 0, 0, 9, 3, 0, 1, 1, 6, 3, 2, 4, 1, 9, 8, 8, 8, 3, 6, 1, 5, 1, 4, 6, 6, 6, 7, 2, 8, 4, 6, 8, 5, 7, 6, 9, 7, 7, 9, 2, 8, 7, 4, 7, 6, 2
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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), 383403.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
N. J. A. Sloane, Table of maximal density of a packing of equal spheres in ndimensional Euclidean space (for n>3 the 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

Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A222073, A222074, A222075.
Sequence in context: A197139 A198367 A021780 * A105388 A178247 A048651
Adjacent sequences: A020766 A020767 A020768 * A020770 A020771 A020772


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane


STATUS

approved



