A272489 Decimal expansion of the edge length of a regular 11-gon with unit circumradius.

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

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 = 11, and the constant, a = e(11), 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 10

Formula

Equals 2*sin(Pi/11) = 2*cos(Pi*9/22).

Example

0.5634651136828593954228358306932337980715557979465337436621606121...

Mathematica

RealDigits[N[2Sin[Pi/11], 100]][[1]] (* Robert Price, May 01 2016 *)

Prog

(PARI) 2*sin(Pi/11)

Crossrefs

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A079267 A060296 A114598 * A259500 A274082 A199666

Adjacent sequences: A272486 A272487 A272488 * A272490 A272491 A272492

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 01 2016

Status

approved