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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-Fran├žois 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...

MATHEMATICA

RealDigits[2*Sin[Pi/5], 10, 120][[1]] (* Harvey P. Dale, Sep 29 2012 *)

PROG

(PARI) 2*sin(Pi/5) \\ Stanislav Sykora, May 02 2016

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 18 22:44 EDT 2018. Contains 316327 sequences. (Running on oeis4.)