cp's OEIS Frontend

A361621 Decimal expansion of the mode of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).

%I A361621 #7 Mar 18 2023 06:54:53
%S A361621 4,0,6,8,1,1,7,8,0,1,7,4,2,0,8,7,7,1,0,1,3,8,4,2,6,8,8,1,1,8,0,8,0,8,
%T A361621 0,3,4,4,4,4,8,6,0,9,2,9,1,3,4,6,2,7,1,7,8,7,2,0,5,0,7,9,6,3,2,3,1,9,
%U A361621 3,8,6,4,8,8,2,0,0,7,9,5,3,9,6,7,2,4,1,0,6,1,5,7,8,6,4,6,0,3,7,0,4,7,0,8,9
%N A361621 Decimal expansion of the mode of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
%C A361621 The value of t where P(t) takes its maximum value, where P(t) is given in A361618.
%C A361621 The corresponding value in degrees is 23.3085980601...
%H A361621 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 A361621 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 A361621 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Mode.html">Mode</a>.
%H A361621 Wikipedia, <a href="https://en.wikipedia.org/wiki/Misorientation">Misorientation</a>.
%e A361621 0.40681178017420877101384268811808080344448609291346...
%t A361621 wp = 200; f[a_] := If[a <= 0 || a >= Pi/4, 0, Sin[a] * (Pi^2/32 - NIntegrate[ArcSin[Tan[a/2]*Cos[x]], {x, 0, Pi/4}, WorkingPrecision -> wp])]; RealDigits[t /. (NMaximize[f[t], {t}, WorkingPrecision -> wp][[2]]), 10, 100][[1]]
%Y A361621 Cf. A228496, A361601, A361618, A361619, A361620.
%K A361621 nonn,cons
%O A361621 0,1
%A A361621 _Amiram Eldar_, Mar 18 2023