A179375 Decimal expansion of the ratio of the chord length of a circular segment with area r^2 of a circle with radius r to r itself.

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

Offset: 1

Author

Rick L. Shepherd, Jul 11 2010

Keywords

• cons
• nonn

Comments

In other words, the chord length is A179375*r. The arc length of the circular segment/sector is r*A179373. The area of the circular segment, r^2, is 1/Pi (A049541) times the area of the circle. The area of the sector is (r^2)*(A179373/2) = (r^2)*(1 + A179378). See references and cross-references for other relationships.

Examples

			1.914359546159529939985785242460527899501301180791115677192453168859627644264...
		

References

• S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 7.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Circular Segment.
• Index entries for transcendental numbers.

Crossrefs

Cf. A179373 (central angle, radians), A179374 (central angle, degrees), A179376 (for "cap height", height of segment), A179377 (for triangle height), A179378 (for triangle area), A049541.

Programs

Mathematica

RealDigits[ 2*Sin[x/2] /. FindRoot[x - Sin[x] - 2, {x, 2}, WorkingPrecision -> 106]][[1]] (* Jean-François Alcover, Oct 30 2012 *)

PARI

2*sin(solve(x=0, Pi, x-sin(x)-2)/2)

Formula

Equals 2*sin(A179373/2).