A348669 - OEIS

%I #10 Oct 29 2021 09:05:28

%S 2,6,4,5,0,5,0,0,7,0,0,7,8,6,9,8,4,5,5,1,5,7,7,5,2,0,1,2,9,7,2,2,5,2,

%T 6,9,3,6,3,4,0,0,0,9,0,9,6,8,0,5,1,8,3,0,5,6,2,2,4,4,3,7,2,5,8,6,4,0,

%U 2,1,3,7,3,7,6,4,3,5,6,7,9,4,6,7,5,8,9,8,3,5,6,9,7,2,3,5,1,3,7,2,5,3,4,3,4

%N Decimal expansion of 2*sqrt(2)*log(1 + sqrt(2))/(3*Pi).

%C The average length of a random line segment in a unit square defined as follows. A line that is making a random angle with a given edge of the square is chosen, and a random distance of this line from a given vertex of this edge is chosen uniformly between 0 and the distance to the opposite vertex in the square. The segment is then being chosen by picking at random two points between the two intersection points of the line with the perimeter of the square.

%H Eric Rosenberg, <a href="https://doi.org/10.1016/S0167-6377(03)00072-5">The expected length of a random line segment in a rectangle</a>, Operations Research Letters, Vol. 32, No. 2 (2004), pp. 99-102.

%e 0.26450500700786984551577520129722526936340009096805...

%p evalf(sqrt(8/9)*arcsinh(1)/Pi, 120);  # _Alois P. Heinz_, Oct 29 2021

%t RealDigits[2*Sqrt[2]*Log[1 + Sqrt[2]]/(3*Pi), 10, 100][[1]]

%o (PARI) 2*sqrt(2)*log(1 + sqrt(2))/(3*Pi) \\ _Michel Marcus_, Oct 29 2021

%Y Cf. A088367, A091505, A091648, A244920.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Oct 29 2021