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%I #25 Jul 29 2020 20:45:58
%S 5,8,6,5,0,3,3,2,8,4,3,3,6,5,5,9,6,2,8,6,6,5,0,5,1,2,6,2,6,5,2,7,2,9,
%T 1,8,9,5,1,9,6,0,1,3,9,7,2,5,0,1,9,5,1,0,4,0,0,4,7,5,4,8,4,7,8,1,7,2,
%U 7,2,7,2,3,9,8,0,4,7,6,5,3,8,6,9,7,1,4,9,7,8,3,8,2,6,2,1,8
%N Decimal expansion of 1-(3*sqrt(3))/(4*Pi).
%C This is the probability that a Gaussian triangle in 3 dimensions is obtuse.
%C Also the probability that the distance between 2 randomly selected points within a circle will be smaller than the radius. - _Amiram Eldar_, Mar 03 2019
%H G. C. Greubel, <a href="/A102519/b102519.txt">Table of n, a(n) for n = 0..5000</a>
%H M. W. Crofton, <a href="https://archive.org/stream/mathematicalque02unkngoog#page/n84/mode/2up">Problem 1829</a>, solved by J. J. Sylvester and by the proposer, Mathematical Questions with Their Solutions: From the "Educational Times", Vol. 4 (1866), pp. 77-78.
%H S. R. Finch, <a href="/A102519/a102519.pdf">Random Triangles</a>, Jan 21 2010. [Cached copy, with permission of the author]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianTrianglePicking.html">Gaussian Triangle Picking</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 0.58650332843365596286650512626527291895196013972501951040047548478172727...
%t RealDigits[1 - (3*Sqrt[3])/(4*Pi), 10, 50][[1]] (* _G. C. Greubel_, Jun 02 2017 *)
%o (PARI) 1 - (3*sqrt(3))/(4*Pi) \\ _G. C. Greubel_, Jun 02 2017
%Y Cf. A102520, A240935.
%K cons,nonn
%O 0,1
%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 13 2005
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