A133742 -id:A133742 - cp's OEIS frontend

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

Rick L. Shepherd, Jul 11 2010

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.

			.71050581697213734990563924269484526760618954800103872979253477385591...

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

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Circular Segment.

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

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

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

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

cp's OEIS Frontend

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.

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