A093524 Decimal expansion of 3977/216000 - Pi^2/2160.

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

Offset: 0

Author

Eric W. Weisstein, Mar 30 2004

Keywords

• nonn
• cons

Comments

Average volume of a tetrahedron picked at random in a unit cube.

From Amiram Eldar, Aug 25 2020: (Start)

The exact value of this constant was first calculated by Zinani (2003).

Equals (1/5) times the probability that 5 points independently and uniformly chosen in a cube are the vertices of a re-entrant (concave) polyhedron, i.e., one of the points falls within the tetrahedron formed by the other 4 points. Do and Solomon (1986) evaluated this probability using simulations, and their result is equivalent to an estimate of 0.0139 of this constant, with a 95% confidence interval of [0.01358, 0.01420] (Zinani, 2003). (End)

Examples

			0.0138427757...
		

Links

• Kim-Anh Do and Herbert Solomon, A simulation study of Sylvester's problem in three dimensions, Journal of applied probability, Vol. 23, No. 2 (1986), pp. 509-513, alternative link.
• Johan Philip, The Expected Volume of a Random Tetrahedron in a Cube, 2007.
• Eric Weisstein's World of Mathematics, Cube Tetrahedron Picking.
• Alessandro Zinani, The expected volume of a tetrahedron whose vertices are chosen at random in the interior of a cube, Monatshefte für Mathematik, Vol. 139, No. 4 (2003), pp. 341-348.
• Index entries for transcendental numbers

Crossrefs

Cf. A093591.

Programs

Mathematica

RealDigits[3977/216000-Pi^2/2160,10,120][[1]] (* Harvey P. Dale, Oct 31 2013 *)

Extensions

Added initial 0 to match offset. - N. J. A. Sloane, Feb 08 2015