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

Author

Rick L. Shepherd, Jul 11 2010

Keywords

• cons
• nonn

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.

Examples

			.2894941830278626500943607573051547323938104519989612702074652261440891212633...
		

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.

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.

Programs

Mathematica

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

PARI

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

Formula

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