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

Author

Eric W. Weisstein, Jan 16 2005

Keywords

• nonn
• cons

Examples

			0.422157733...
		

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

Programs

Mathematica

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

PARI

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

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))).