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

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allocatedDecimal 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 forthan Amiramthe Eldarradius.

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

-2,1

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.

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

0.0034180050840544470129780521403541151709450230941762...

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

Cf. A102519, A240935, A324558.

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Amiram Eldar, Mar 06 2019

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