A179374 - OEIS

%I #9 Feb 24 2023 05:31:21

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

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

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

%N Decimal expansion of the central angle in degrees corresponding to a circular segment with area r^2 of a circle with radius r.

%C 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="/A179374/b179374.txt">Table of n, a(n) for n = 3..10002</a>

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

%F Equals A179373*180/Pi = A179373*A072097.

%e 146.3446481469584283647321150080224451316690962652634500095885765914885737881...

%t RealDigits[(180/Pi)*(x /.FindRoot[x-Sin[x]-2, {x, 2}, WorkingPrecision -> 200]), 10, 100][[1]] (* _G. C. Greubel_, Nov 16 2018 *)

%o (PARI) (solve(x=0, Pi, x-sin(x)-2))*180/Pi

%Y Cf. A179373 (same, in radians), A179375 (for chord length), A179376 (for "cap height", height of segment), A179377 (for triangle height), A179378 (for triangle area), A049541.

%K cons,nonn

%O 3,2

%A _Rick L. Shepherd_, Jul 11 2010