OFFSET
1,1
LINKS
Steven R. Finch, Three Random Tangents to a Circle, arXiv:1101.3931 (math.PR], 2011.
FORMULA
Side length density for x>2 is p(x) = (16/Pi^2)*((x*arctan((x + sqrt(x^2 - 4))/2) - x*arctan((x - sqrt(x^2 - 4))/2) + log((x + sqrt(x^2 - 4))/(x - sqrt(x^2 - 4))))/((x^2 + 4)*x)).
EXAMPLE
5.548203918878445277644299718216988498950141170649469975237323384077...
MATHEMATICA
digits = 104; p[x_] := (16/Pi^2)*((x*ArcTan[(x + Sqrt[x^2 - 4])/2] - x*ArcTan[(x - Sqrt[x^2 - 4])/2] + Log[(x + Sqrt[x^2 - 4])/(x - Sqrt[x^2 - 4])])/((x^2 + 4)*x)); P[x_?NumericQ] := NIntegrate[p[t], {t, 2, x}, WorkingPrecision -> digits + 5]; m = x /. FindRoot[P[x] == 1/2, {x, 5}, WorkingPrecision -> digits + 5]; First[RealDigits[m, 10, digits]]
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jean-François Alcover, Aug 15 2015
STATUS
approved