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 A019881 Decimal expansion of sin(2*Pi/5) (sine of 72 degrees). 21
 9, 5, 1, 0, 5, 6, 5, 1, 6, 2, 9, 5, 1, 5, 3, 5, 7, 2, 1, 1, 6, 4, 3, 9, 3, 3, 3, 3, 7, 9, 3, 8, 2, 1, 4, 3, 4, 0, 5, 6, 9, 8, 6, 3, 4, 1, 2, 5, 7, 5, 0, 2, 2, 2, 4, 4, 7, 3, 0, 5, 6, 4, 4, 4, 3, 0, 1, 5, 3, 1, 7, 0, 0, 8, 5, 1, 9, 3, 5, 0, 1, 7, 1, 8, 7, 9, 2, 8, 1, 0, 9, 7, 0, 8, 1, 1, 3, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Circumradius of pentagonal pyramid (Johnson solid 2) with edge 1. - Vladimir Joseph Stephan Orlovsky, Jul 19 2010 Circumscribed sphere radius for a regular icosahedron with unit edges. - Stanislav Sykora, Feb 10 2014 Side length of the particular golden rhombus with diagonals 1 and phi (A001622); area is phi/2 (A019863). Thus, also the ratio side/(shorter diagonal) for any golden rhombus. Interior angles of a golden rhombus are always A105199 and A137218. - Rick L. Shepherd, Apr 10 2017 An algebraic number of degree 4; minimal polynomial is 16x^4 - 20x^2 + 5, which has these smaller, other solutions (conjugates): -A019881 < -A019845 < A019845 (sine of 36 degrees). - Rick L. Shepherd, Apr 11 2017 This is length ratio of one half of any diagonal in the regular pentagon and the circumscribing radius. - Wolfdieter Lang, Jan 07 2018 LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Golden Rhombus Wikipedia, Exact trigonometric constants Wikipedia, Platonic solid Wolfram Alpha, Johnson solid 2 FORMULA Equals sqrt((5+sqrt(5))/8) = cos(Pi/10). - Zak Seidov, Nov 18 2006 Equals 2F1(13/20,7/20;1/2;3/4) / 2. - R. J. Mathar, Oct 27 2008 Equals the real part of i^(1/5). - Stanislav Sykora, Apr 25 2012 Equals A001622*A182007/2. - Stanislav Sykora, Feb 10 2014 Equals sin(2*Pi/5) = sqrt(2 + phi)/2 = sin(3*Pi/5), with phi = A001622  - Wolfdieter Lang, Jan 07 2018 EXAMPLE 0.95105651629515357211643933337938214340569863412575022244730564443015317008... MAPLE Digits:=100: evalf(sin(2*Pi/5)); # Wesley Ivan Hurt, Sep 01 2014 MATHEMATICA RealDigits[Sqrt[(5 + Sqrt[5])/8], 10, 111]  (* Robert G. Wilson v *) RealDigits[Sin[2 Pi/5], 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *) PROG (PARI) default(realprecision, 120); real(I^(1/5)) // Rick L. Shepherd, Apr 10 2017 (MAGMA) SetDefaultRealField(RealField(100)); Sqrt((5 + Sqrt(5))/8); // G. C. Greubel, Nov 02 2018 CROSSREFS Cf. A001622, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A182007. Cf. Platonic solids circumradii: A010503 (octahedron), A010527 (cube), A179296 (dodecahedron), A187110 (tetrahedron). - Stanislav Sykora, Feb 10 2014 Sequence in context: A197378 A232738 A201395 * A049256 A256191 A019982 Adjacent sequences:  A019878 A019879 A019880 * A019882 A019883 A019884 KEYWORD nonn,cons AUTHOR STATUS approved

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Last modified December 18 08:16 EST 2018. Contains 318219 sequences. (Running on oeis4.)