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A330924
Decimal expansion of the mean length of a line segment drawn by picking a random point on a unit square and extending it in a random direction until it meets an edge.
0
4, 7, 3, 2, 0, 1, 0, 0, 4, 4, 0, 9, 3, 3, 8, 5, 5, 1, 6, 4, 2, 4, 9, 8, 2, 0, 9, 7, 6, 3, 0, 1, 1, 9, 8, 1, 2, 9, 9, 9, 6, 0, 5, 6, 8, 9, 6, 3, 6, 3, 4, 9, 8, 2, 3, 7, 2, 6, 3, 6, 6, 1, 4, 3, 3, 8, 5, 9, 8, 6, 7, 5, 7, 2, 7, 3, 4, 2, 9, 6, 1, 5, 0, 8, 0, 6, 9, 5, 3, 2, 5, 5, 3, 0, 4, 6, 7, 5, 0, 5, 3, 1, 9, 4, 1, 0, 5, 5
OFFSET
0,1
LINKS
FORMULA
Equals (2 - 2 * sqrt(2)) / (3 * Pi) + (2 / Pi) * cosech^{-1}(1)
Equals (a^3 + b^3 - d^3) / (3 * Pi * a * b) + (a / Pi) * cosech^{-1}(a / b) + (b / Pi) * cosech^{-1}(b / a) for an arbitrary rectangle with sides a, b and diagonal d.
EXAMPLE
0.47320100440933855164249820976301198129996056896363...
MATHEMATICA
N[(2 - 2 Sqrt[2])/3/Pi + 2 ArcCsch[1]/Pi, 50]
PROG
(PARI) arcsch(x) = log(1/x + sqrt(1+1/x^2));
(2 - 2*sqrt(2))/(3*Pi) + (2/ Pi)*arcsch(1) \\ Michel Marcus, Jan 16 2020
CROSSREFS
Cf. A330646.
Sequence in context: A200602 A118823 A118826 * A165663 A254397 A197697
KEYWORD
nonn,cons
AUTHOR
STATUS
approved