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.
FORMULA
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
KEYWORD
AUTHOR
Eric W. Weisstein, Apr 16 2004
EXTENSIONS
Entry revised by N. J. A. Sloane, Feb 10 2013
STATUS
approved