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

%I A093591 #12 Feb 16 2025 08:32:53
%S A093591 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 A093591 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 A093591 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 A093591 Decimal expansion of (12*Pi)/715.
%C A093591 Mean volume of a tetrahedron formed by four random points in a unit ball.
%C A093591 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 A093591 Bohuslav Hostinský, Sur les probabilités géométriques, Brno: Publications de la Faculté des sciences de l'Université Masaryk, 1925.
%H A093591 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 A093591 Herbert Solomon, <a href="https://archive.org/details/GeometricProbability/page/n133/mode/2up">Geometric Probability</a>, Philadelphia, PA: SIAM, 1978, p. 124.
%H A093591 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BallTetrahedronPicking.html">Ball Tetrahedron Picking</a>.
%H A093591 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A093591 0.0527260305...
%t A093591 RealDigits[12*Pi/715, 10, 100][[1]] (* _Amiram Eldar_, Aug 25 2020 *)
%o A093591 (PARI) 12*Pi/715 \\ _Charles R Greathouse IV_, Sep 30 2022
%Y A093591 Cf. A093524.
%K A093591 nonn,cons
%O A093591 0,2
%A A093591 _Eric W. Weisstein_, Apr 02 2004