A179376 - OEIS

%I #13 Feb 24 2023 05:31:32

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%D S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 7.

%H G. C. Greubel, <a href="/A179376/b179376.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CircularSegment.html">Circular Segment</a>.

%F Equals 1 - cos(A179373/2) = 1 - A179377.

%e .71050581697213734990563924269484526760618954800103872979253477385591...

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

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

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

%K cons,nonn

%O 0,1

%A _Rick L. Shepherd_, Jul 11 2010