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%I #11 Mar 06 2021 02:24:22
%S 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 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 0,7,6,4,6,4,5,7,1,0,5,1,1,0,1,0,1,7
%N Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.
%C 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 *****************
%C Guide to related sequences:
%C arclength,s ratio, A1/A2
%C 1/3 A336073
%C Pi/6 A336074
%C Pi/5 A336075
%C Pi/4 A336076
%C Pi/3 A336077
%C Pi/2 A336078
%C 1 A336079
%C 2 A336080
%C 3 A336081
%C *****************
%C ratio, A1/A2 arclength, s
%C 2 A336082
%C 3 A336083
%C 4 A336084
%C 5 A336085
%C 1/2 A336086
%F ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = 1/3.
%e ratio = 1022.54737393604920361975925805839994393435790826122033281
%t s = 1/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
%t RealDigits[r][[1]]
%Y Cf. A336059-A336086.
%K nonn,cons
%O 4,3
%A _Clark Kimberling_, Jul 10 2020
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