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A336085
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.
1
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, 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, 7, 4, 9, 7, 3, 3, 3, 8, 1, 4, 7, 2, 6, 0, 4, 7, 0, 3
OFFSET
1,2
COMMENTS
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.
EXAMPLE
arclength = 1.96896871291852970013017702612056418255322313061290398752...
MATHEMATICA
k = 5; s = s /. FindRoot[(2 Pi - s + Sin[s])/(s - Sin[s]) == k, {s, 2}, WorkingPrecision -> 200]
RealDigits[s][[1]]
CROSSREFS
Cf. A336073.
Sequence in context: A161484 A103985 A153071 * A363539 A086279 A155533
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 11 2020
STATUS
approved