A120671 Decimal expansion of arccos(1-8/(Pi^2)) / (2*Pi).

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

Offset: 0

Author

Rick L. Shepherd, Jun 22 2006

Keywords

• cons
• nonn

Comments

The average arc length between two randomly chosen points on a circle of radius r is r*A120669 corresponding to the average chord length r*A088538. (Each arc averaged is no larger than the semicircle.). This sequence is the ratio of that average arc length to the circumference (and is thus also the ratio of the corresponding sector's area to the circle's area).

Examples

			0.219667909710056641181661197550...
		

Crossrefs

Cf. A088538, A120669 (2*Pi*A120671), A120670 (360*A120671).

Programs

Mathematica

RealDigits[ArcCos[(1-(8/(Pi^2) ))]/(2Pi),10,120][[1]] (* Harvey P. Dale, Jun 17 2018 *)

PARI

acos(1-8/Pi^2)/(2*Pi)

Formula

Equals A120669/(2*Pi) = A120670/360.