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

0,1

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

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. 15, line n = 3.

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.

Formula

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

Example

0.74048048969306104116931349834344894976910361489594837...

Mathematica

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

Prog

(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

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.

Sequence in context: A175998 A329091 A306398 * A229784 A374814 A091494

Adjacent sequences: A093822 A093823 A093824 * A093826 A093827 A093828

Keyword

nonn,cons,easy

Author

Eric W. Weisstein, Apr 16 2004

Extensions

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

Status

approved