OFFSET
0,1
COMMENTS
Length of the rope in the "goat outside the fence" version of the grazing goat problem, when the radius of the circular field is assumed to be 1. See Fraser (1982) for details. - Hugo Pfoertner, Apr 05 2020
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
M. Fraser, A tale of two goats, Math. Mag., 55 (1982), 221-227.
FORMULA
Equals (z + 1/z - 1)*Pi/2 where x = 6/Pi^2 - 1 and z = (x - sqrt(x^2 - 1))^(1/3). - Peter Luschny, Apr 05 2020
EXAMPLE
0.91508964079634209342198381417593107109296289714973860113292...
MATHEMATICA
RealDigits[Pi*(Cos[ArcCos[6/Pi^2 -1]/3] -1/2), 10, 100][[1]] (* G. C. Greubel, Feb 06 2019 *)
PROG
(PARI) Pi*cos(acos(6/Pi^2-1)/3) - Pi/2 \\ Michel Marcus, Sep 19 2017
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*( Cos(Arccos(6/Pi(R)^2 -1)/3) -1/2); // G. C. Greubel, Feb 06 2019
(Sage) numerical_approx(pi*(cos(acos(6/pi^2 -1)/3) - 1/2), digits=100) # G. C. Greubel, Feb 06 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Jul 12 2011
STATUS
approved