login
Decimal expansion of the probability of intersection of 2 random chords in a circle, where each chord is selected by 2 random points within the circle.
3

%I #10 Apr 09 2018 10:07:26

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

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

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

%N Decimal expansion of the probability of intersection of 2 random chords in a circle, where each chord is selected by 2 random points within the circle.

%H Herbert Solomon, <a href="https://archive.org/stream/GeometricProbability/Geometric_Probability-Solomon#page/n161/mode/2up">Geometric Probability</a>, SIAM, 1978, p. 153.

%F 1/3 + 245/(72*Pi^2)

%e 0.67810680544962158338542317342198988238288749714861...

%t RealDigits[1/3 + 245/(72*Pi^2), 10, 100][[1]]

%o (PARI) 1/3 + 245/(72*Pi^2) \\ _Altug Alkan_, Mar 28 2018

%Y Cf. A301862, A301864, A301865.

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Mar 28 2018