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
Examples
0.91508964079634209342198381417593107109296289714973860113292...
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.
Programs
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Magma
SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*( Cos(Arccos(6/Pi(R)^2 -1)/3) -1/2); // G. C. Greubel, Feb 06 2019
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Mathematica
RealDigits[Pi*(Cos[ArcCos[6/Pi^2 -1]/3] -1/2), 10, 100][[1]] (* G. C. Greubel, Feb 06 2019 *)
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PARI
Pi*cos(acos(6/Pi^2-1)/3) - Pi/2 \\ Michel Marcus, Sep 19 2017
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Sage
numerical_approx(pi*(cos(acos(6/pi^2 -1)/3) - 1/2), digits=100) # G. C. Greubel, Feb 06 2019
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
Comments