cp's OEIS Frontend

A192930 Decimal expansion of Pi*cos(phi) - Pi/2, where phi is the constant defined by A191102.

%I A192930 #19 Sep 08 2022 08:45:58
%S A192930 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 A192930 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 A192930 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 A192930 Decimal expansion of Pi*cos(phi) - Pi/2, where phi is the constant defined by A191102.
%C A192930 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 A192930 G. C. Greubel, <a href="/A192930/b192930.txt">Table of n, a(n) for n = 0..10000</a>
%H A192930 M. Fraser, <a href="http://www.jstor.org/stable/2690163">A tale of two goats</a>, Math. Mag., 55 (1982), 221-227.
%F A192930 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 A192930 0.91508964079634209342198381417593107109296289714973860113292...
%t A192930 RealDigits[Pi*(Cos[ArcCos[6/Pi^2 -1]/3] -1/2), 10, 100][[1]] (* _G. C. Greubel_, Feb 06 2019 *)
%o A192930 (PARI) Pi*cos(acos(6/Pi^2-1)/3) - Pi/2 \\ _Michel Marcus_, Sep 19 2017
%o A192930 (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 A192930 (Sage) numerical_approx(pi*(cos(acos(6/pi^2 -1)/3) - 1/2), digits=100) # _G. C. Greubel_, Feb 06 2019
%Y A192930 Cf. A133731, A173201.
%K A192930 nonn,cons
%O A192930 0,1
%A A192930 _N. J. A. Sloane_, Jul 12 2011