cp's OEIS Frontend

A019693 Decimal expansion of 2*Pi/3.

%I A019693 #66 Jul 02 2025 01:02:35
%S A019693 2,0,9,4,3,9,5,1,0,2,3,9,3,1,9,5,4,9,2,3,0,8,4,2,8,9,2,2,1,8,6,3,3,5,
%T A019693 2,5,6,1,3,1,4,4,6,2,6,6,2,5,0,0,7,0,5,4,7,3,1,6,6,2,9,7,2,8,2,0,5,2,
%U A019693 1,0,9,3,7,5,2,4,1,3,9,3,3,2,4,1,8,6,8,9,8,8,3,5,6,1,4,1,1,3,7
%N A019693 Decimal expansion of 2*Pi/3.
%C A019693 Volume between a cylinder and the inscribed sphere of radius 1. - _Omar E. Pol_, Sep 25 2013
%C A019693 (2/3)*Pi is also the surface area of a sphere whose diameter equals the square root of 2/3. More generally, x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - _Omar E. Pol_, Jun 18 2018
%C A019693 Volume of a hemisphere of radius 1. - _Omar E. Pol_, Aug 17 2019
%C A019693 Angle in radians between two vectors of equal magnitude and originating from the same point whose vector sum also has the same magnitude. - _Stefano Spezia_, Jun 30 2025
%H A019693 Ivan Panchenko, <a href="/A019693/b019693.txt">Table of n, a(n) for n = 1..1000</a>
%H A019693 Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, pp. 235-236.
%H A019693 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A019693 Equals 5*A019699. - _Omar E. Pol_, Aug 17 2019
%F A019693 Equals arccos(-1/2). - _Amiram Eldar_, Aug 12 2020
%F A019693 Equals Integral_{x=-oo..oo} 1/(1 + x^6) dx. - _Stefano Spezia_, Mar 05 2022
%F A019693 Equals Integral_{x=0..2*Pi} 1/(5 - 4*cos(x)) dx. - _Kritsada Moomuang_, May 22 2025
%e A019693 2.094395102393195492308428922186335256131446... - _Omar E. Pol_, Sep 25 2013
%t A019693 RealDigits[N[2*Pi/3, 6!]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009 *)
%o A019693 (PARI) 2*Pi/3 \\ _Michel Marcus_, Jun 19 2018
%Y A019693 Cf. A000796, A019692, A019699, A157697.
%K A019693 nonn,cons
%O A019693 1,1
%A A019693 _N. J. A. Sloane_