A102888 Decimal expansion of volume of the Reuleaux tetrahedron.

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

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Definite Integral

Eric Weisstein's World of Mathematics, Reuleaux Tetrahedron

Formula

(8/3)*Pi - (27/4)*arccos(1/3) + sqrt(2)/4

= (3*sqrt(2) - 49*Pi + 162*arctan(sqrt(2)))/12

= (1/24)*(6*sqrt(2) + 16*Pi + 57*arccos(17/81) - 132*arctan(sqrt(2))).

Example

0.422157733...

Mathematica

RealDigits[8 Pi/3 - 27 ArcSec[3]/4 + Sqrt[2]/4, 10, 102][[1]] (* Eric W. Weisstein, Dec 15 2017 *)

Prog

(PARI) 8/3*Pi - (27/4)*acos(1/3) + sqrt(2)/4 \\ Michel Marcus, Dec 15 2017

Crossrefs

Sequence in context: A264752 A325527 A088570 * A071558 A179621 A350788

Adjacent sequences: A102885 A102886 A102887 * A102889 A102890 A102891

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 16 2005

Status

approved