A020769 Decimal expansion of 1/sqrt(12) = 1/(2*sqrt(3)).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

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

Examples

			0.28867513459481288225457439025097872782380087563506343800930116324198883615...
		

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
• Index entries for algebraic numbers, degree 2

Crossrefs

Related constants: A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A260646.

Programs

Mathematica

RealDigits[N[1/Sqrt[12],200]] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)

PARI

1/sqrt(12) \\ Charles R Greathouse IV, Oct 31 2014