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

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, 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, 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

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

Cf. A133731, A173201.

Sequence in context: A089101 A359809 A298512 * A010168 A340004 A327963

Adjacent sequences: A192927 A192928 A192929 * A192931 A192932 A192933

Keyword

nonn,cons

Author

N. J. A. Sloane, Jul 12 2011

Status

approved