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

Author

Clark Kimberling, Jul 11 2020

Keywords

• nonn
• cons

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.

Examples

			33.68074644435052842991251795285920080736045858...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A336073.

Programs

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]]

Formula

Equals (2*Pi - s + sin(s))/(s - sin(s)), where s = Pi/3 = A019670.