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

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).

Minimal polynomial: x^18 - 19*x^16 + 152*x^14 - 665*x^12 + 1729*x^10 - 2717*x^8 + 2508*x^6 - 1254*x^4 + 285*x^2 - 19. - Amiram Eldar, Jun 06 2026

Example

0.32918918056146778828730411817587683902434496671930824670294254...

Mathematica

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

Prog

(PARI) 2*sin(Pi/19)

Crossrefs

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18).

Sequence in context: A228492 A340875 A329038 * A010271 A291777 A143074

Adjacent sequences: A272488 A272489 A272490 * A272492 A272493 A272494

Keyword

nonn,cons,easy,changed

Author

Stanislav Sykora, May 01 2016

Status

approved