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A182007
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Decimal expansion of 2*sin(Pi/5); the 'associate' of the golden ratio.
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17
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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
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OFFSET
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1,3
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COMMENTS
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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).
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.
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LINKS
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Eric Weisstein's World of Mathematics, Pentagon
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FORMULA
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c = 2*sin(Pi/5) = sqrt(3-phi).
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EXAMPLE
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1.1755705045849462583374119...
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MAPLE
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MATHEMATICA
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RealDigits[2*Sin[Pi/5], 10, 120][[1]] (* Harvey P. Dale, Sep 29 2012 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2*Sin(Pi(R)/5); // G. C. Greubel, Nov 02 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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