A336077 - OEIS

%I #24 Oct 01 2022 15:42:15

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

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

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

%N Decimal expansion of (10*Pi + 3*sqrt(3)) / (2*Pi - 3*sqrt(3)).

%C Decimal expansion of the ratio of segment areas for arclength Pi/3 on the unit circle. In general, suppose that s in (0,Pi) is the length of an arc of the unit circle. The associated chord separates the interior into two segments. Let A1 be the area of the larger and A2 the area of the smaller. The term "ratio of segment areas" means A1/A2. See A336073 for a guide to related sequences.

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

%F Equals (2*Pi - s + sin(s))/(s - sin(s)), where s = Pi/3 = A019670.

%e 33.68074644435052842991251795285920080736045858...

%p s := Pi/3 ;

%p sss := s-sin(s) ;

%p evalf( 2*Pi/sss -1 ) ; # _R. J. Mathar_, Sep 02 2020

%t s = Pi/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]

%t RealDigits[r][[1]]

%Y Cf. A336073.

%K nonn,cons

%O 2,1

%A _Clark Kimberling_, Jul 11 2020