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A179373 Decimal expansion of the central angle in radians corresponding to a circular segment with area r^2 of a circle with radius r. 6
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Weisstein, Eric W., "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-Fran├žois 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 A116698

Adjacent sequences:  A179370 A179371 A179372 * A179374 A179375 A179376

KEYWORD

cons,nonn

AUTHOR

Rick L. Shepherd, Jul 11 2010

STATUS

approved

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Last modified October 23 00:24 EDT 2020. Contains 337962 sequences. (Running on oeis4.)