

A093825


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


20



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
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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 facecenteredcubic (fcc) and the hexagonalclosepacked (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. xix.
Clifford A. Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (2009), at 126.


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), 383403.
T. C. Hales, Home Page (see under Dense Sphere Packings
G. Nebe and N. J. A. Sloane, Home page for fcc lattice
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).
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


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=(xd)*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.  Harry J. Smith, Jun 18 2009
Related constants: A020769, A020789, A093766, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A222073, A222074, A222075.
Sequence in context: A303982 A175998 A306398 * A229784 A091494 A021139
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



