A182007 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A182007

Decimal expansion of 2*sin(Pi/5).

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

The 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.

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.

Index entries for algebraic numbers, degree 4.

FORMULA

c = 2*sin(Pi/5) = sqrt(3-phi).

Equals sqrt((5-sqrt(5))/2). - Jean-François Alcover, May 21 2013

Equals Product_{k>=0} ((10*k + 4)*(10*k + 6))/((10*k + 3)*(10*k + 7)). - Antonio Graciá Llorente, Mar 25 2024

EXAMPLE

1.1755705045849462583374119...