A272491 - OEIS

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A272491

Decimal expansion of the edge length of a regular 19-gon with unit circumradius.

3, 2, 9, 1, 8, 9, 1, 8, 0, 5, 6, 1, 4, 6, 7, 7, 8, 8, 2, 8, 7, 3, 0, 4, 1, 1, 8, 1, 7, 5, 8, 7, 6, 8, 3, 9, 0, 2, 4, 3, 4, 4, 9, 6, 6, 7, 1, 9, 3, 0, 8, 2, 4, 6, 7, 0, 2, 9, 4, 2, 5, 4, 8, 0, 9, 8, 1, 5, 3, 8, 0, 5, 7, 0, 4, 9, 4, 3, 4, 1, 2, 5, 9, 5, 5, 7, 4, 6, 2, 8, 7, 6, 0, 1, 8, 7, 9, 8, 6, 0, 7, 7, 2, 8, 5

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OFFSET

0,1

COMMENTS

The edge length e(m) of a regular m-gon is e(m) = 2*sin(Pi/m). In this case, m = 19, and the constant, a = e(19), is not constructible using a compass and a straightedge (see A004169). With an odd m, in fact, e(m) would be constructible only if m were a Fermat prime (A019434).

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Constructible number

Wikipedia, Regular polygon

Index entries for algebraic numbers, degree 18

FORMULA

Equals 2*sin(Pi/19) = 2*cos(Pi*17/38).

EXAMPLE

0.32918918056146778828730411817587683902434496671930824670294254...

MATHEMATICA

RealDigits[N[2Sin[Pi/19], 100]][[1]] (* Robert Price, May 01 2016 *)

PROG