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%I #10 Mar 06 2021 02:22:33
%S 1,9,6,8,9,6,8,7,1,2,9,1,8,5,2,9,7,0,0,1,3,0,1,7,7,0,2,6,1,2,0,5,6,4,
%T 1,8,2,5,5,3,2,2,3,1,3,0,6,1,2,9,0,3,9,8,7,5,2,3,4,7,1,7,3,1,9,5,2,2,
%U 7,4,9,7,3,3,3,8,1,4,7,2,6,0,4,7,0,3
%N Decimal expansion of the arclength on the unit circle such that the corresponding chord separates the interior into segments having 5 = ratio of segment areas; 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. See A336073 for a guide to related sequences.
%e arclength = 1.96896871291852970013017702612056418255322313061290398752...
%t k = 5; s = s /. FindRoot[(2 Pi - s + Sin[s])/(s - Sin[s]) == k, {s, 2}, WorkingPrecision -> 200]
%t RealDigits[s][[1]]
%Y Cf. A336073.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Jul 11 2020
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