A361620 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).

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, 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, 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

Offset

0,1

Comments

The corresponding value in degrees is 23.1834079659...

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, Median.

Wikipedia, Misorientation.

Formula

Equals c such that Integral_{t=0..c} P(t) dt = 1/2, where P(t) is given in the Formula section of A361618.

Example

0.40462680083850138475144500357414183647267233632878...

Mathematica

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]]

Crossrefs

Cf. A228496, A361601, A361618, A361619, A361621.

Sequence in context: A134944 A088375 A217220 * A303560 A341481 A135011

Adjacent sequences: A361617 A361618 A361619 * A361621 A361622 A361623

Keyword

nonn,cons

Author

Amiram Eldar, Mar 18 2023

Status

approved