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).

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, 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, 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

Offset: 0

Author

Amiram Eldar, Mar 18 2023

Keywords

• nonn
• cons

Comments

The value of t where P(t) takes its maximum value, where P(t) is given in A361618.

The corresponding value in degrees is 23.3085980601...

Examples

			0.40681178017420877101384268811808080344448609291346...
		

Links

• J. K. Mackenzie, Second Paper on Statistics Associated with the Random Disorientation of Cubes, Biometrika, Vol. 45, No. 1-2 (1958), pp. 229-240.
• J. K. Mackenzie and M. J. Thomson, Some Statistics Associated with the Random Disorientation of Cubes, Biometrika, Vol. 44, No. 1-2 (1957), pp. 205-210.
• Eric Weisstein's World of Mathematics, Mode.
• Wikipedia, Misorientation.

Crossrefs

Cf. A228496, A361601, A361618, A361619, A361620.

Programs

Mathematica

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]]