

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.


6



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
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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 crossreferences for other relationships.


REFERENCES

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


LINKS



FORMULA



EXAMPLE

.71050581697213734990563924269484526760618954800103872979253477385591...


MATHEMATICA

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


PROG

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


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



