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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
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
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Jul 11 2010
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)