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A336043
Decimal expansion of the solution s of s/c = 3/2, where s = arclength and c = chord length on the unit circle.
15
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
OFFSET
1,1
COMMENTS
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
FORMULA
s = 2.9915631364441994204309876991519194313413...
c = 1.9943754242961329469539917994346129542275...
MATHEMATICA
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 *)
CROSSREFS
Cf. A336044.
Sequence in context: A011072 A175295 A198141 * A340723 A201765 A160331
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 06 2020
STATUS
approved