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A336077
Decimal expansion of (10*Pi + 3*sqrt(3)) / (2*Pi - 3*sqrt(3)).
1
3, 3, 6, 8, 0, 7, 4, 6, 4, 4, 4, 3, 5, 0, 5, 2, 8, 4, 2, 9, 9, 1, 2, 5, 1, 7, 9, 5, 2, 8, 5, 9, 2, 0, 0, 8, 0, 7, 3, 6, 0, 4, 5, 8, 5, 8, 5, 3, 2, 3, 3, 8, 8, 4, 5, 0, 7, 6, 4, 3, 5, 5, 3, 4, 8, 7, 4, 0, 7, 9, 1, 1, 1, 2, 2, 3, 5, 6, 8, 0, 4, 2, 1, 1, 1, 4
OFFSET
2,1
COMMENTS
Decimal expansion of the ratio of segment areas for arclength Pi/3 on the unit circle. In general, 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
Equals (2*Pi - s + sin(s))/(s - sin(s)), where s = Pi/3 = A019670.
EXAMPLE
33.68074644435052842991251795285920080736045858...
MAPLE
s := Pi/3 ;
sss := s-sin(s) ;
evalf( 2*Pi/sss -1 ) ; # R. J. Mathar, Sep 02 2020
MATHEMATICA
s = Pi/3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]
CROSSREFS
Cf. A336073.
Sequence in context: A367394 A298732 A078477 * A360375 A098832 A368151
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 11 2020
STATUS
approved