A272488 Decimal expansion of the edge length of a regular 9-gon with unit circumradius.

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

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 = 9, and the constant, a = e(9), 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 6

Formula

Equals 2*sin(Pi/9) = 2*cos(Pi*7/18) = 2*A019829.

Equals Im((4+4*sqrt(3)*i)^(1/3)). - Gerry Martens, Mar 19 2024

Example

0.6840402866513374660881992293645191615261667350283212569300969953...

Mathematica

RealDigits[N[2Sin[Pi/9], 100]][[1]] (* Robert Price, May 01 2016 *)

Prog

(PARI) 2*sin(Pi/9)

Crossrefs

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A272487 (n=7), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A184084 A346402 A255728 * A100608 A350795 A352769

Adjacent sequences: A272485 A272486 A272487 * A272489 A272490 A272491

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 01 2016

Status

approved