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A336073
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Decimal expansion of the ratio of segment areas for arclength 1/3 on the unit circle; see Comments.
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14
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1, 0, 2, 2, 5, 4, 7, 3, 7, 3, 9, 3, 6, 0, 4, 9, 2, 0, 3, 6, 1, 9, 7, 5, 9, 2, 5, 8, 0, 5, 8, 3, 9, 9, 9, 4, 3, 9, 3, 4, 3, 5, 7, 9, 0, 8, 2, 6, 1, 2, 2, 0, 3, 3, 2, 8, 1, 0, 3, 5, 8, 1, 6, 0, 4, 5, 3, 5, 0, 7, 6, 4, 6, 4, 5, 7, 1, 0, 5, 1, 1, 0, 1, 0, 1, 7
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OFFSET
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4,3
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COMMENTS
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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.
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Guide to related sequences:
arclength,s ratio, A1/A2
1/3 A336073
Pi/6 A336074
Pi/5 A336075
Pi/4 A336076
Pi/3 A336077
Pi/2 A336078
1 A336079
2 A336080
3 A336081
*****************
ratio, A1/A2 arclength, s
2 A336082
3 A336083
4 A336084
5 A336085
1/2 A336086
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LINKS
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Table of n, a(n) for n=4..89.
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FORMULA
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ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = 1/3.
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EXAMPLE
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ratio = 1022.54737393604920361975925805839994393435790826122033281
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MATHEMATICA
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s = 1/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]
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CROSSREFS
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Cf. A336059-A336086.
Sequence in context: A261114 A284827 A241306 * A266792 A162200 A290289
Adjacent sequences: A336070 A336071 A336072 * A336074 A336075 A336076
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Jul 10 2020
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STATUS
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approved
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