A179373 - OEIS

A179373

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

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

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OFFSET

1,1

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 = 1..10000

Eric Weisstein's World of Mathematics, Circular Segment.

FORMULA

Decimal expansion of the solution of sin(x) = x - 2.

EXAMPLE

2.5541959528370430378296661737918779361157491714110524381405663643020...

MATHEMATICA

RealDigits[ x /. FindRoot[x - Sin[x] - 2, {x, 2}, WorkingPrecision -> 105]][[1]] (* Jean-François Alcover, Oct 30 2012 *)

PROG

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

CROSSREFS

Cf. A179374 (same, in degrees), A179375 (for chord length), A179376 (for "cap height", height of segment), A179377 (for triangle height), A179378 (for triangle area), A049541.

Sequence in context: A004582 A074269 A198542 * A200484 A197004 A363764

Adjacent sequences: A179370 A179371 A179372 * A179374 A179375 A179376

KEYWORD

cons,nonn

AUTHOR

Rick L. Shepherd, Jul 11 2010

STATUS

approved