OFFSET
0,1
COMMENTS
This constant is the packing density of a regular octahedron. That is, let S be a regular octahedron of edge length 2 and let B the part of S that lies within distance 1 of some vertex. Then this constant is the ratio of the volume of B to the volume of S.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..2000
Thomas C. Hales, A proof of the Kepler conjecture. In: Annals of Mathematics 162 (2005), nr. 3, p. 1065-1185.
EXAMPLE
0.7209029495...
MATHEMATICA
First@ RealDigits@ N[-Sqrt[2] ArcTan[Sqrt[2]/5] + 1/4 Pi Sqrt[2], 120] (* Michael De Vlieger, Jan 09 2016 *)
PROG
(PARI) -sqrt(2)*atan(sqrt(2)/5)+1/4*Pi*sqrt(2) \\ Altug Alkan, Jul 30 2018
(Magma) R:= RealField(); [-Sqrt(2)*Arctan(Sqrt(2)/5) + Pi(R)*Sqrt(2)/4]; // G. C. Greubel, Aug 16 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Martin Renner, Jan 09 2016
STATUS
approved