A179377 Decimal expansion of the ratio of the height of the triangle corresponding to a circular segment with area r^2 of a circle with radius r to r itself.

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

Offset

0,1

Comments

In other words, the triangle height is A179377*r. The segment height ("cap height" in MathWorld link) is A179376*r. The chord length is A179375*r. 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 = 0..10000

Eric Weisstein's World of Mathematics, Circular Segment.

Formula

Equals cos(A179373/2) = 1 - A179376.

Example

.2894941830278626500943607573051547323938104519989612702074652261440891212633...

Mathematica

RealDigits[ Cos[x/2] /. FindRoot[x - Sin[x] - 2, {x, 1}, WorkingPrecision -> 106]][[1]] (* Jean-François Alcover, Oct 30 2012 *)

Prog

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

Crossrefs

Cf. A179373 (central angle, radians), A179374 (central angle, degrees), A179375 (for chord length), A179376 (for "cap height", height of segment), A179378 (for triangle area), A049541.

Sequence in context: A155922 A201896 A154859 * A199274 A140241 A340536

Adjacent sequences: A179374 A179375 A179376 * A179378 A179379 A179380

Keyword

cons,nonn

Author

Rick L. Shepherd, Jul 11 2010

Status

approved