A336077 Decimal expansion of (10*Pi + 3*sqrt(3)) / (2*Pi - 3*sqrt(3)).

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.

Links

Table of n, a(n) for n=2..87.

Index entries for transcendental numbers

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

Adjacent sequences: A336074 A336075 A336076 * A336078 A336079 A336080

Keyword

nonn,cons

Author

Clark Kimberling, Jul 11 2020

Status

approved