cp's OEIS Frontend

A336073 Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.

%I A336073 #13 Feb 22 2025 19:18:05
%S A336073 1,0,2,2,5,4,7,3,7,3,9,3,6,0,4,9,2,0,3,6,1,9,7,5,9,2,5,8,0,5,8,3,9,9,
%T A336073 9,4,3,9,3,4,3,5,7,9,0,8,2,6,1,2,2,0,3,3,2,8,1,0,3,5,8,1,6,0,4,5,3,5,
%U A336073 0,7,6,4,6,4,5,7,1,0,5,1,1,0,1,0,1,7
%N A336073 Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.
%C A336073 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.
%C A336073 *****************
%C A336073 Guide to related sequences:
%C A336073 arclength,s   ratio, A1/A2
%C A336073 1/3           A336073
%C A336073 Pi/6          A336074
%C A336073 Pi/5          A336075
%C A336073 Pi/4          A336076
%C A336073 Pi/3          A336077
%C A336073 Pi/2          A336078
%C A336073 1             A336079
%C A336073 2             A336080
%C A336073 3             A336081
%C A336073 *****************
%C A336073 ratio, A1/A2  arclength, s
%C A336073 2             A336082
%C A336073 3             A336083
%C A336073 4             A336084
%C A336073 5             A336085
%C A336073 1/2           A336086
%F A336073 ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = 1/3.
%e A336073 ratio = 1022.54737393604920361975925805839994393435790826122033281
%t A336073 s = 1/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
%t A336073 RealDigits[r][[1]]
%o A336073 (PARI) 2*Pi/(1/3 - sin(1/3)) - 1 \\ _Charles R Greathouse IV_, Feb 22 2025
%Y A336073 Cf. A336059-A336086.
%K A336073 nonn,cons
%O A336073 4,3
%A A336073 _Clark Kimberling_, Jul 10 2020