A179376 Decimal expansion of the ratio of the height of a circular segment with area r^2 of a circle with radius r to r itself.

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

Offset

0,1

Comments

In other words, 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 1 - cos(A179373/2) = 1 - A179377.

Example

.71050581697213734990563924269484526760618954800103872979253477385591...

Mathematica

RealDigits[1-x /. FindRoot[x == Cos[1+x*Sqrt[1-x^2]], {x, 0}, WorkingPrecision -> 120]][[1]] (* Jean-François Alcover, Oct 06 2011 *)

Prog

(PARI) 1 - cos(solve(x=0, Pi, x-sin(x)-2)/2)

Crossrefs

Cf. A179373 (central angle, radians), A179374 (central angle, degrees), A179375 (for chord length), A179377 (for triangle height), A179378 (for triangle area), A133742, A049541.

Sequence in context: A195911 A231096 A240907 * A152447 A198611 A298853

Adjacent sequences: A179373 A179374 A179375 * A179377 A179378 A179379

Keyword

cons,nonn

Author

Rick L. Shepherd, Jul 11 2010

Status

approved