A222070 Decimal expansion of (1/144)*3^(1/2)*Pi^3.

3, 7, 2, 9, 4, 7, 5, 4, 5, 5, 8, 2, 0, 6, 4, 9, 3, 9, 5, 6, 3, 4, 7, 7, 5, 5, 8, 6, 7, 9, 9, 5, 8, 1, 0, 6, 3, 9, 3, 6, 6, 4, 7, 9, 7, 2, 6, 8, 3, 8, 7, 3, 6, 3, 1, 1, 1, 4, 0, 4, 0, 6, 5, 5, 9, 7, 2, 8, 3, 1, 7, 2, 0, 2, 9, 6, 8, 3, 2, 1, 9, 5, 2, 2, 5, 2, 6, 7, 2, 1, 6, 3, 5, 3, 4, 0, 5, 4, 2, 7, 6

Offset: 0

Author

N. J. A. Sloane, Feb 10 2013

Keywords

• nonn
• cons

Comments

Conjectured to be density of densest packing of equal spheres in six dimensions (achieved for example by the E_6 lattice).

Examples

			0.3729475455820649395634775586799581063936647972683873631...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.

Links

• 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 E_6 lattice.
• 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).
• Index entries for transcendental numbers.

Crossrefs

Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222071, A222072, A260646.

Programs

Mathematica

RealDigits[Sqrt[3]*Pi^3/144, 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)

PARI

Pi^3*sqrt(3)/144 \\ Charles R Greathouse IV, Oct 31 2014