A266814 Decimal expansion of -sqrt(2)*arctan(sqrt(2)/5) + Pi*sqrt(2)/4.

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

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.

Formula

Equals -sqrt(2)*arctan(sqrt(2)/5) + Pi*sqrt(2)/4.

Equals (3*A093825 - A267040)/2.

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

Cf. A093825, A267033, A267040.

Sequence in context: A236565 A093954 A177703 * A200338 A351480 A378699

Adjacent sequences: A266811 A266812 A266813 * A266815 A266816 A266817

Keyword

nonn,cons

Author

Martin Renner, Jan 09 2016

Status

approved