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%I #11 Sep 30 2022 23:39:03
%S 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,
%T 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,
%U 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
%N Decimal expansion of (12*Pi)/715.
%C Mean volume of a tetrahedron formed by four random points in a unit ball.
%C 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
%D Bohuslav Hostinský, Sur les probabilités géométriques, Brno: Publications de la Faculté des sciences de l'Université Masaryk, 1925.
%H Fernando Affentranger, <a href="https://doi.org/10.1111/j.1365-2818.1988.tb04688.x">The expected volume of a random polytope in a ball</a>, Journal of Microscopy, Vol. 151, No. 3 (1988), pp. 277-287.
%H Herbert Solomon, <a href="https://archive.org/details/GeometricProbability/page/n133/mode/2up">Geometric Probability</a>, Philadelphia, PA: SIAM, 1978, p. 124.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BallTetrahedronPicking.html">Ball Tetrahedron Picking</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 0.0527260305...
%t RealDigits[12*Pi/715, 10, 100][[1]] (* _Amiram Eldar_, Aug 25 2020 *)
%o (PARI) 12*Pi/715 \\ _Charles R Greathouse IV_, Sep 30 2022
%Y Cf. A093524.
%K nonn,cons
%O 0,2
%A _Eric W. Weisstein_, Apr 02 2004
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