A179374 Decimal expansion of the central angle in degrees corresponding to a circular segment with area r^2 of a circle with radius r.

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

Offset: 3

Author

Rick L. Shepherd, Jul 11 2010

Keywords

• cons
• nonn

Comments

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

			146.3446481469584283647321150080224451316690962652634500095885765914885737881...
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 3..10002
• Eric Weisstein's World of Mathematics, Circular Segment.

Crossrefs

Cf. A179373 (same, in radians), A179375 (for chord length), A179376 (for "cap height", height of segment), A179377 (for triangle height), A179378 (for triangle area), A049541.

Programs

Mathematica

RealDigits[(180/Pi)*(x /.FindRoot[x-Sin[x]-2, {x, 2}, WorkingPrecision -> 200]), 10, 100][[1]] (* G. C. Greubel, Nov 16 2018 *)

PARI

(solve(x=0, Pi, x-sin(x)-2))*180/Pi

Formula

Equals A179373*180/Pi = A179373*A072097.