login
Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to a corner: (4+log(27))/12.
0

%I #18 May 27 2021 06:31:40

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

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

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

%N Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to a corner: (4+log(27))/12.

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

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

%F Equals Sum_{k>=1} k/((2*k-1)*2^(2*k-1)). - _Amiram Eldar_, May 27 2021

%e 0.607986405500360756182144642563964759495205972789020696267006916742706906637985...

%t RealDigits[(4 + Log[27])/12, 10, 100][[1]] (* _Amiram Eldar_, May 27 2021 *)

%o (PARI) (4+log(27))/12 \\ _Charles R Greathouse IV_, Apr 20 2016

%Y Cf. A245698.

%K nonn,cons

%O 0,1

%A _Derek Orr_, Jul 29 2014