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

1,2

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.

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.

Formula

Equals 2*sin(A179373/2).

Example

1.914359546159529939985785242460527899501301180791115677192453168859627644264...

Mathematica

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

Prog

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

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.

Sequence in context: A176520 A011462 A335533 * A089564 A178745 A114893

Adjacent sequences: A179372 A179373 A179374 * A179376 A179377 A179378

Keyword

cons,nonn

Author

Rick L. Shepherd, Jul 11 2010

Status

approved