A336081 Decimal expansion of the ratio of segment areas for arclength 3 on the unit circle; see Comments.

1, 1, 9, 7, 7, 7, 8, 6, 1, 4, 3, 1, 5, 1, 8, 2, 9, 7, 0, 9, 1, 1, 0, 6, 4, 7, 3, 2, 9, 9, 0, 8, 0, 0, 8, 9, 1, 2, 5, 8, 5, 1, 0, 8, 9, 4, 5, 9, 9, 3, 4, 6, 3, 8, 1, 5, 6, 3, 4, 9, 2, 2, 2, 5, 1, 3, 7, 2, 5, 3, 6, 0, 5, 3, 5, 1, 2, 2, 9, 2, 2, 5, 0, 0, 2, 2

Offset: 1

Author

Clark Kimberling, Jul 11 2020

Keywords

• nonn
• cons

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.

Examples

			ratio = 1.19777861431518297091106473299080089125851089...
		

Crossrefs

Cf. A336073.

Programs

Mathematica

s = 3; r = N[(2 Pi - s + Sin[s])/(s - Sin[s]), 200]
RealDigits[r][[1]]

Formula

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