A395844 - OEIS

%I #4 May 09 2026 04:56:22

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

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

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

%N Decimal expansion of the expected distance of a point uniformly selected at random in the interior of a unit-side equilateral triangle to its farthest vertex.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals (27*log(3) + sqrt(3)*(4 + 3*log(3)) - 6*sqrt(3)*arcsinh(sqrt(3)))/36.

%e 0.79480733322987534391386667022183944873388881213248...

%t RealDigits[(27*Log[3] + Sqrt[3]*(4 + 3*Log[3]) - 6*Sqrt[3]*ArcSinh[Sqrt[3]])/36, 10, 120][[1]]

%o (PARI) (27*log(3) + sqrt(3)*(4 + 3*log(3)) - 6*sqrt(3)*asinh(sqrt(3)))/36

%Y Cf. A065918, A093064, A245698, A245700, A395843, A395845 (square).

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 08 2026