A324559 - OEIS

%I #7 Mar 15 2019 23:03:50

%S 3,4,1,8,0,0,5,0,8,4,0,5,4,4,4,7,0,1,2,9,7,8,0,5,2,1,4,0,3,5,4,1,1,5,

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

%U 0,5,2,0,4,1,2,3,5,9,6,0,0,8,2,6,1,1,1

%N Decimal expansion of the probability that the length of a chord drawn through 2 points taken at random within a circle on each side of a given diameter will be less than the radius.

%H J. J. Sylvester, <a href="https://archive.org/stream/mathematicalque26unkngoog#page/n96/mode/2up">Problem 1849</a>, solved by Stephen Watson, Mathematical Questions with Their Solutions: From the "Educational Times", Vol. 8 (1868), pp. 92-93.

%F Equals 13/144 - 13*sqrt(3)/(48*Pi) + 3*(3 + log(4/3))/(16*Pi^2).

%e 0.0034180050840544470129780521403541151709450230941762...

%t RealDigits[13/144-13*Sqrt[3]/(48*Pi)+3*(3+Log[4/3])/(16*Pi^2),10,100][[1]]

%Y Cf. A102519, A240935, A324558.

%K nonn,cons

%O -2,1

%A _Amiram Eldar_, Mar 06 2019