A272490 Decimal expansion of the edge length of a regular 13-gon with unit circumradius.

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

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 = 13, and the constant, a = e(13), 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 12

Formula

Equals 2*sin(Pi/13) = 2*cos(Pi*11/26).

Example

0.47863132857511553429750745252042379040634604547661202671031943...

Mathematica

RealDigits[N[2Sin[Pi/13], 100]][[1]] (* Robert Price, May 01 2016 *)

Prog

(PARI) 2*sin(Pi/13)

Crossrefs

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A154687 A115021 A200367 * A261654 A332504 A121488

Adjacent sequences: A272487 A272488 A272489 * A272491 A272492 A272493

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 01 2016

Status

approved