A093825 Decimal expansion of Pi/(3*sqrt(2)).

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

Offset: 0

Author

Eric W. Weisstein, Apr 16 2004

Keywords

• nonn
• cons
• easy

Comments

Density of densest packing of equal spheres in three dimensions (achieved for example by the fcc lattice).

Atomic packing factor (APF) of the face-centered-cubic (fcc) and the hexagonal-close-packed (hcp) crystal lattices filled with spheres of the same diameter. - Stanislav Sykora, Sep 29 2014

Examples

			0.74048048969306104116931349834344894976910361489594837...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. 15, line n = 3.
• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 506.
• Clifford A. Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (2009), at p. 126.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 29.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• James Grime and Brady Haran, The Best Way to Pack Spheres, Numberphile video (2018).
• 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.
• Thomas C. Hales, Dense Sphere Packings, Cambridge University Press, 2012.
• G. Nebe and N. J. A. Sloane, Home page for fcc 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).
• Eric Weisstein's World of Mathematics, Cubic Close Packing.
• Eric Weisstein's World of Mathematics, Ellipsoid Packing.
• Eric Weisstein's World of Mathematics, Sphere Packing.
• Wikipedia, Atomic packing factor.
• Index entries for sequences related to f.c.c. lattice.
• Index entries for transcendental numbers.

Crossrefs

Cf. A093824.

Cf. APF's of other crystal lattices: A019673 (simple cubic), A247446 (diamond cubic).

Cf. A161686 (continued fraction).

Related constants: A020769, A020789, A093766, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A260646.

Programs

Mathematica

RealDigits[Pi/(3 Sqrt[2]), 10, 120][[1]] (* Harvey P. Dale, Feb 03 2012 *)

PARI

default(realprecision, 20080); x=10*Pi*sqrt(2)/6; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b093825.txt", n, " ", d)); \\ Harry J. Smith, Jun 18 2009

PARI

Pi/sqrt(18) \\ Charles R Greathouse IV, May 11 2017

Formula

Equals A019670*A010503. - R. J. Mathar, Feb 05 2009

Equals Integral_{x >= 0} (4*x^2 + 1)/((2*x^2 + 1)*(8*x^2 + 1)) dx. - Peter Bala, Feb 12 2025

Extensions

Entry revised by N. J. A. Sloane, Feb 10 2013