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Decimal expansion of Pi*cos(phi) - Pi/2, where phi is the constant defined by A191102.
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%I #19 Sep 08 2022 08:45:58

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

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

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

%N Decimal expansion of Pi*cos(phi) - Pi/2, where phi is the constant defined by A191102.

%C 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

%H G. C. Greubel, <a href="/A192930/b192930.txt">Table of n, a(n) for n = 0..10000</a>

%H M. Fraser, <a href="http://www.jstor.org/stable/2690163">A tale of two goats</a>, Math. Mag., 55 (1982), 221-227.

%F 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

%e 0.91508964079634209342198381417593107109296289714973860113292...

%t RealDigits[Pi*(Cos[ArcCos[6/Pi^2 -1]/3] -1/2), 10, 100][[1]] (* _G. C. Greubel_, Feb 06 2019 *)

%o (PARI) Pi*cos(acos(6/Pi^2-1)/3) - Pi/2 \\ _Michel Marcus_, Sep 19 2017

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*( Cos(Arccos(6/Pi(R)^2 -1)/3) -1/2); // _G. C. Greubel_, Feb 06 2019

%o (Sage) numerical_approx(pi*(cos(acos(6/pi^2 -1)/3) - 1/2), digits=100) # _G. C. Greubel_, Feb 06 2019

%Y Cf. A133731, A173201.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Jul 12 2011