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

0,1

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...

Links

Table of n, a(n) for n=0..104.

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.

Example

0.40681178017420877101384268811808080344448609291346...

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]]

Crossrefs

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

Sequence in context: A333479 A361211 A155743 * A354491 A262246 A194193

Adjacent sequences: A361618 A361619 A361620 * A361622 A361623 A361624

Keyword

nonn,cons

Author

Amiram Eldar, Mar 18 2023

Status

approved