A272487 Decimal expansion of the edge length of a regular heptagon with unit circumradius.

8, 6, 7, 7, 6, 7, 4, 7, 8, 2, 3, 5, 1, 1, 6, 2, 4, 0, 9, 5, 1, 5, 3, 6, 6, 6, 5, 6, 9, 6, 7, 1, 7, 5, 0, 9, 2, 1, 9, 9, 8, 1, 4, 5, 5, 5, 7, 4, 9, 1, 9, 7, 5, 2, 8, 8, 9, 0, 9, 4, 6, 0, 7, 0, 6, 4, 4, 0, 6, 5, 0, 3, 3, 0, 6, 3, 9, 6, 8, 4, 3, 0, 4, 1, 5, 6, 8, 0, 4, 3, 5, 4, 8, 9, 1, 2, 2, 0, 4, 1, 7, 7, 4, 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 = 7, and the constant, a = e(7), is the smallest m for which e(m) 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, Heptagon

Wikipedia, Regular polygon

Index entries for algebraic numbers, degree 6

Formula

Equals 2*sin(Pi/7) = 2*cos(Pi*5/14).

Equals i^(-5/7) + i^(5/7). - Gary W. Adamson, Feb 12 2022

Example

0.8677674782351162409515366656967175092199814555749197528890946...

Mathematica

N[2*Sin[Pi/7], 25] (* G. C. Greubel, May 01 2016 *)
RealDigits[2*Sin[Pi/7], 10, 120][[1]] (* Harvey P. Dale, Mar 07 2020 *)

Prog

(PARI) 2*sin(Pi/7)

Crossrefs

Cf. A004169, A019434.

Cf. A160389.

Edge lengths of nonconstructible n-gons: A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A182369 A104175 A019792 * A020828 A378968 A011465

Adjacent sequences: A272484 A272485 A272486 * A272488 A272489 A272490

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 01 2016

Status

approved