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%I #14 Mar 06 2021 02:03:33
%S 2,9,9,1,5,6,3,1,3,6,4,4,4,1,9,9,4,2,0,4,3,0,9,8,7,6,9,9,1,5,1,9,1,9,
%T 4,3,1,3,4,1,3,4,9,4,1,4,2,0,7,8,6,9,3,0,1,7,1,5,5,8,3,0,1,9,4,8,2,0,
%U 9,3,1,6,4,7,9,9,2,7,9,4,6,7,2,1,5,0
%N Decimal expansion of the solution s of s/c = 3/2, where s = arclength and c = chord length on the unit circle.
%C For every constant k > 1, the ratio s/c such that s/c = k is the same for all circles. Choosing the unit circle, x^2 + y^2 = 1, we have c = sqrt(2 - 2*cos(s)), so that the solution of s/c = k is the solution of s = k*sqrt(2 - 2*cos(s)). For each s in (0, 2*Pi) there is a unique solution c; for each c in (0, Pi), there are two solutions s; if one of them is s_0, the other is 2*Pi - s_0.
%C Guide to related sequences:
%C ratio, s/c arclength, s chord length, c
%C 3/2 A336043 A336044
%C 2 A336045 A199460
%C 3 A336047 A336048
%C Pi A336049 A336050
%C 4 A336051 A336052
%C 5 A336053 A336054
%C 6 A336055 A336056
%C 2*Pi A336057 A336058
%F s = 2.9915631364441994204309876991519194313413...
%F c = 1.9943754242961329469539917994346129542275...
%t t = t /.FindRoot[t == (3/2) Sqrt[2 - 2 Cos[t]], {t, 4}, WorkingPrecision -> 200]
%t c = 2 t/3
%t RealDigits[t][[1]] (* A336043 *)
%t RealDigits[c][[1]] (* A336044 *)
%Y Cf. A336044.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Jul 06 2020