%I #9 May 25 2023 03:09:37

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

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

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

%N Decimal expansion of the mean length of a line segment picked at random in a 30-60-90 (right) triangle.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/30-60-90Triangle.html">30-60-90 Triangle</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangleLinePicking.html">Triangle Line Picking</a>.

%F Equals (204 + 36*sqrt(3) + 81*log(3) + 2*(9 + 8*sqrt(3))*log(2 + sqrt(3)))/1440.

%e 0.28857171834839485625...

%t RealDigits[(204 + 36*Sqrt[3] + 81*Log[3] + 2*(9 + 8*Sqrt[3])*Log[2 + Sqrt[3]])/1440, 10, 120][[1]] (* _Amiram Eldar_, May 25 2023 *)

%Y Cf. A093063, A093064, A180307.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Aug 25 2010