cp's OEIS Frontend

A330646 Decimal expansion of the mean length of a line segment drawn by picking a random point on a unit length equilateral triangle and extending it in a random direction until it meets an edge.

%I A330646 #13 Dec 23 2019 13:10:22
%S A330646 3,0,2,8,4,8,3,4,9,8,0,4,0,9,7,9,3,3,3,7,5,6,9,1,3,0,3,4,9,2,5,6,4,5,
%T A330646 7,0,8,8,4,5,9,6,9,9,0,5,7,8,2,8,5,8,1,4,5,5,8,5,0,9,2,5,3,5,1,6,3,4,
%U A330646 0,5,1,4,4,9,4,4,5,2,5,0,2,3,3,1,0,1,1,4,7,6,0,0,2,2,6,2,0,4,3,1,8,0,3,1,7,3,8,8,6,7
%N A330646 Decimal expansion of the mean length of a line segment drawn by picking a random point on a unit length equilateral triangle and extending it in a random direction until it meets an edge.
%H A330646 Muthu Veerappan Ramalingam, <a href="https://am-just-a-nobody.blogspot.com/2017/09/an-expected-value-problem-iii.html">An Expected Value Problem III</a>
%F A330646 Equals sqrt(3) * log(3) / (2 * Pi).
%F A330646 Equals (h_a/(3*Pi))*cosech^{-1}((1/2)*((b+c)/a-a/(b+c)))+(h_b/(3*Pi))*cosech^{-1}((1/2)*((c+a)/b-b/(c+a)))+(h_c/(3*Pi))*cosech^{-1}((1/2)*((a+b)/c-c/(a+b))) for an arbitrary triangle with sides a, b and c with corresponding altitudes h_a, h_b and h_c.
%e A330646 0.302848349804097933375691303492564570884596990578285814558...
%t A330646 RealDigits[Sqrt[3] Log[3]/2/Pi, 10, 110][[1]]
%Y A330646 Cf. A093064.
%K A330646 nonn,cons
%O A330646 0,1
%A A330646 _Muthu Veerappan Ramalingam_, Dec 22 2019