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A336074
Decimal expansion of the ratio of segment areas for arclength Pi/6 on the unit circle; see Comments.
1
2, 6, 5, 2, 5, 0, 4, 7, 9, 0, 1, 3, 5, 1, 7, 6, 4, 7, 7, 1, 2, 5, 4, 8, 1, 8, 5, 4, 9, 2, 5, 4, 0, 0, 8, 9, 5, 3, 8, 4, 3, 5, 1, 6, 0, 9, 0, 5, 2, 3, 9, 1, 2, 8, 0, 2, 3, 9, 3, 9, 4, 0, 7, 4, 4, 8, 0, 1, 2, 5, 2, 0, 1, 5, 2, 8, 8, 2, 0, 1, 9, 0, 0, 6, 1, 4
OFFSET
3,1
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.
FORMULA
ratio = (2*Pi - s + sin(s))/(s - sin(s)), where s = Pi/6.
EXAMPLE
ratio = 265.25047901351764771254818549254008953843516090523...
MATHEMATICA
s = Pi/6; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]
CROSSREFS
Cf. A336073.
Sequence in context: A271533 A335995 A304585 * A021381 A323501 A157890
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 10 2020
STATUS
approved