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