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%I #7 Nov 23 2021 09:02:31
%S 3,5,0,9,5,9,3,1,2,1,8,3,6,4,3,6,2,1,0,2,5,1,3,3,3,5,5,3,3,4,5,8,5,4,
%T 6,7,8,9,9,7,7,1,8,9,6,6,3,6,4,0,1,7,2,3,7,2,7,6,2,9,7,8,8,1,3,2,0,0,
%U 8,4,5,2,0,6,4,6,5,3,4,8,1,2,2,1,2,7,0,9,5,7,0,5,4,6,4,7,0,7,8,4,7,7,1,6,0
%N Decimal expansion of the probability that the intersection of a cube with random plane that passes through its center is a hexagon.
%C The normal to the random plane is in the direction from the center of the cube to a point uniformly chosen at random on the surface of a sphere whose center coincides with the center of the cube.
%H Su Pernu Mero, <a href="https://doi.org/10.1080/0025570X.2019.1544816">Problem 2065</a>, Mathematics Magazine, Vol. 92, No. 1, (2019), p. 73; <a href="https://doi.org/10.1080/0025570X.2020.1685297">Solution</a>, by Bill Cowieson, ibid., Vol. 93, No. 1 (2020), pp. 76-77.
%H Yawen Zhang, <a href="https://arxiv.org/abs/2010.12349">A purely 3-D geometrical solution to Mathematics Magazine Problem 2065</a>, arXiv:2010.12349 [math.HO], 2020.
%F Equals 1 - 6*arcsin(1/3)/Pi.
%F Equals 6*arccos(1/3)/Pi - 2.
%e 0.35095931218364362102513335533458546789977189663640...
%t RealDigits[1 - 6 * ArcSin[1/3] / Pi, 10, 100][[1]]
%o (PARI) 1 - 6*asin(1/3)/Pi \\ _Michel Marcus_, Nov 23 2021
%Y Cf. A137914, A188615.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Nov 23 2021