A093591 Decimal expansion of (12*Pi)/715.

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

Offset: 0

Author

Eric W. Weisstein, Apr 02 2004

Keywords

• nonn
• cons

Comments

Mean volume of a tetrahedron formed by four random points in a unit ball.

Equals (4*Pi/15) times the probability (9/143) that 5 points independently and uniformly chosen in a ball 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. It was calculated by the Czech physicist and mathematician Bohuslav Hostinský (1884 - 1951) in 1925. - Amiram Eldar, Aug 25 2020

Examples

			0.0527260305...
		

References

• Bohuslav Hostinský, Sur les probabilités géométriques, Brno: Publications de la Faculté des sciences de l'Université Masaryk, 1925.

Links

• Fernando Affentranger, The expected volume of a random polytope in a ball, Journal of Microscopy, Vol. 151, No. 3 (1988), pp. 277-287.
• Herbert Solomon, Geometric Probability, Philadelphia, PA: SIAM, 1978, p. 124.
• Eric Weisstein's World of Mathematics, Ball Tetrahedron Picking.
• Index entries for transcendental numbers

Crossrefs

Cf. A093524.

Programs

Mathematica

RealDigits[12*Pi/715, 10, 100][[1]] (* Amiram Eldar, Aug 25 2020 *)

PARI

12*Pi/715 \\ Charles R Greathouse IV, Sep 30 2022