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

3,2

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.

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.

Formula

Equals A179373*180/Pi = A179373*A072097.

Example

146.3446481469584283647321150080224451316690962652634500095885765914885737881...

Mathematica

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

Prog

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

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.

Sequence in context: A200365 A198121 A244020 * A081709 A200640 A179453

Adjacent sequences: A179371 A179372 A179373 * A179375 A179376 A179377

Keyword

cons,nonn

Author

Rick L. Shepherd, Jul 11 2010

Status

approved