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A019881
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Decimal expansion of sin(2*Pi/5) (sine of 72 degrees).
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29
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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
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OFFSET
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0,1
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COMMENTS
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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
This gives the imaginary part of one of the members of a conjugate pair of roots of x^5 - 1, with real part (-1 + phi)/2 = A019827, where phi = A001622. A member of the other conjugte pair of roots is (-phi + sqrt(3 - phi)*i)/2 = (-A001622 + A182007*i)/2 = -A001622/2 + A019845*i. - Wolfdieter Lang, Aug 30 2022
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LINKS
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FORMULA
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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
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EXAMPLE
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0.95105651629515357211643933337938214340569863412575022244730564443015317008...
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MAPLE
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MATHEMATICA
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PROG
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(PARI)
default(realprecision, 120);
(Magma) SetDefaultRealField(RealField(100)); Sqrt((5 + Sqrt(5))/8); // G. C. Greubel, Nov 02 2018
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CROSSREFS
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Cf. A001622, A019827, A102208, A179290 (inverse), A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A182007.
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KEYWORD
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AUTHOR
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STATUS
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approved
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