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A336043
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Decimal expansion of the solution s of s/c = 3/2, where s = arclength and c = chord length on the unit circle.
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15
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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, 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, 9, 3, 1, 6, 4, 7, 9, 9, 2, 7, 9, 4, 6, 7, 2, 1, 5, 0
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OFFSET
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1,1
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COMMENTS
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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.
Guide to related sequences:
ratio, s/c arclength, s chord length, c
3/2 A336043 A336044
2 A336045 A199460
3 A336047 A336048
Pi A336049 A336050
4 A336051 A336052
5 A336053 A336054
6 A336055 A336056
2*Pi A336057 A336058
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LINKS
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Table of n, a(n) for n=1..86.
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FORMULA
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s = 2.9915631364441994204309876991519194313413...
c = 1.9943754242961329469539917994346129542275...
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MATHEMATICA
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t = t /.FindRoot[t == (3/2) Sqrt[2 - 2 Cos[t]], {t, 4}, WorkingPrecision -> 200]
c = 2 t/3
RealDigits[t][[1]] (* A336043 *)
RealDigits[c][[1]] (* A336044 *)
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CROSSREFS
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Cf. A336044.
Sequence in context: A011072 A175295 A198141 * A340723 A201765 A160331
Adjacent sequences: A336040 A336041 A336042 * A336044 A336045 A336046
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Jul 06 2020
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STATUS
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approved
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