This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361618 #12 Aug 09 2025 03:35:11
%S A361618 4,0,4,2,8,3,3,4,5,0,4,4,8,9,3,5,8,5
%N A361618 Decimal expansion of the mean of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
%C A361618 The angle in degrees is 23.1637293985...
%H A361618 Amiram Eldar, <a href="/A361618/a361618.txt">Mathematica code for A361618 and A361619</a>.
%H A361618 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 A361618 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 A361618 Wikipedia, <a href="https://en.wikipedia.org/wiki/Misorientation">Misorientation</a>.
%F A361618 Equals Integral_{t=0..arccos(2/3)} t * P(t) dt, where P(t) = P1(t) if 0 <= t <= Pi/4, and P1(t) + P2(t) if Pi/4 < t <= arccos(2/3), and where
%F A361618 P1(t) = (288/Pi^2) * sin(t) * (Pi^2/32 - Integral_{x=0..Pi/4} arcsin(tan(t/2)*cos(x)) dx),
%F A361618 P2(t) = -(288/Pi^2) * sin(t) * (Pi*g(t)/4 - Integral_{x=Pi/4-g(t)..Pi/8+g(t)} arcsin(tan(t/2)*cos(x)) dx),
%F A361618 g(t) = arcsin(sqrt(((sqrt(2) + 1)^2 * tan(t/2)^2 - 1)/(4 * sqrt(2) * tan(t/2)^2))).
%e A361618 0.404283345044893585...
%t A361618 (* See the program in the links section. *)
%Y A361618 Cf. A228496, A361601, A361619, A361620, A361621.
%K A361618 nonn,cons,more
%O A361618 0,1
%A A361618 _Amiram Eldar_, Mar 18 2023