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%I #6 Mar 19 2023 08:29:28
%S 4,0,4,6,2,6,8,0,0,8,3,8,5,0,1,3,8,4,7,5,1,4,4,5,0,0,3,5,7,4,1,4,1,8,
%T 3,6,4,7,2,6,7,2,3,3,6,3,2,8,7,8,7,1,8,8,0,0,2,1,0,5,9,0,6,4,9,0,1,2,
%U 9,7,2,4,8,6,7,3,5,2,3,2,0,8,3,1,7,2,2,6,8,7,8,9,1,7,1,8,2,7,8,7,9,1,0,9,7
%N Decimal expansion of the median of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
%C The corresponding value in degrees is 23.1834079659...
%H J. K. Mackenzie, <a href="http://www.jstor.org/stable/2333059">Second Paper on Statistics Associated with the Random Disorientation of Cubes</a>, Biometrika, Vol. 45, No. 1-2 (1958), pp. 229-240.
%H J. K. Mackenzie and M. J. Thomson, <a href="http://www.jstor.org/stable/2333253">Some Statistics Associated with the Random Disorientation of Cubes</a>, Biometrika, Vol. 44, No. 1-2 (1957), pp. 205-210.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Median.html">Median</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Misorientation">Misorientation</a>.
%F Equals c such that Integral_{t=0..c} P(t) dt = 1/2, where P(t) is given in the Formula section of A361618.
%e 0.40462680083850138475144500357414183647267233632878...
%t wp = 110; p[a_?NumericQ] := If[a <= 0 || a >= Pi/4, 0, (288/Pi^2) * Sin[a]*(Pi^2/32 - NIntegrate[ArcSin[Tan[a/2]*Cos[x]], {x, 0, Pi/4}, WorkingPrecision -> wp])]; f[y_?NumericQ] := NIntegrate[p[a], {a, 0, y}, WorkingPrecision -> wp]; RealDigits[y /. FindRoot[f[y] == 1/2, {y, 0.5}, WorkingPrecision -> wp], 10, 100][[1]]
%Y Cf. A228496, A361601, A361618, A361619, A361621.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Mar 18 2023
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