%I #16 Feb 12 2024 01:47:43

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

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

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

%N Decimal expansion of 2*sqrt(3)/(3*Pi).

%C The ratio of the volume of a cube to the volume of the circumscribed sphere (which has circumradius a*sqrt(3)/2 = a*A010527, where a is the cube's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165953, and A165954. A063723 shows the order of these by size.

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

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

%F 2*sqrt(3)/(3*Pi) = 2*A002194/(3*A000796) = 3*A165922 = (2*sqrt(3)/3)*A049541 = 10*A020832*A049541 = 2*A020760*A049541.

%e 0.3675525969478613663408843322086462942649243202444271018662440135273535356...

%t RealDigits[(2*Sqrt[3])/(3Pi),10,120][[1]] (* _Harvey P. Dale_, Oct 08 2012 *)

%o (PARI) 2*sqrt(3)/(3*Pi)

%Y Cf. A000796, A002194, A165922, A049541, A165953, A165954, A063723, A020760, A020832.

%K cons,nonn

%O 0,1

%A _Rick L. Shepherd_, Oct 02 2009