OFFSET
0,1
COMMENTS
The corresponding value in degrees is 23.1834079659...
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, 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
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 18 2023
STATUS
approved