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 A182007 Decimal expansion of 2*sin(Pi/5); the 'associate' of the golden ratio. 14
 1, 1, 7, 5, 5, 7, 0, 5, 0, 4, 5, 8, 4, 9, 4, 6, 2, 5, 8, 3, 3, 7, 4, 1, 1, 9, 0, 9, 2, 7, 8, 1, 4, 5, 5, 3, 7, 1, 9, 5, 3, 0, 4, 8, 7, 5, 2, 8, 6, 2, 9, 1, 9, 8, 2, 1, 4, 4, 5, 4, 4, 9, 6, 1, 5, 1, 4, 5, 5, 6, 9, 4, 8, 3, 2, 4, 7, 0, 3, 9, 1, 5, 0, 1, 7, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Golden ratio phi is the real part of 2*exp(i*Pi/5), while this constant c is the corresponding imaginary part. It is handy, for example, in simplifying metric expressions for Platonic solids (particularly for regular icosahedron and dodecahedron). Note that c^2+A001622^2 = 4; c*A001622 = A188593 = 2*A019881; c = 2*A019845. Equals sqrt((5-sqrt(5))/2), which is the eccentricity of a golden ellipse, that is, an ellipse inscribed in a golden rectangle. - Jean-François Alcover, May 21 2013 Edge length of a regular pentagon with unit circumradius. - Stanislav Sykora, May 07 2014 This is a constructible number (see A003401 for more details). Moreover, since phi is also constructible, (2^k)*exp(i*Pi/5), for any integer k, is a constructible complex number. - Stanislav Sykora, May 02 2016 rms(c, phi) := sqrt((c^2+phi^2)/2) = sqrt(2) = A002193. LINKS Ivan Panchenko, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Pentagon Wikipedia, Platonic solid FORMULA c = 2*sin(Pi/5) = sqrt(3-phi). EXAMPLE 1.1755705045849462583374119... MAPLE evalf(2*sin(Pi/5), 100); # Muniru A Asiru, Nov 02 2018 MATHEMATICA RealDigits[2*Sin[Pi/5], 10, 120][] (* Harvey P. Dale, Sep 29 2012 *) PROG (PARI) 2*sin(Pi/5) \\ Stanislav Sykora, May 02 2016 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); 2*Sin(Pi(R)/5); // G. C. Greubel, Nov 02 2018 CROSSREFS Cf. A001622, A002193, A003401, A019881, A019845, A102769, A131595, A188593. Sequence in context: A070273 A158244 A226580 * A247320 A179294 A259679 Adjacent sequences:  A182004 A182005 A182006 * A182008 A182009 A182010 KEYWORD nonn,cons,easy AUTHOR Stanislav Sykora, Apr 06 2012 STATUS approved

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Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)