A272487 - OEIS

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

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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

One of the 6 real-valued roots of x^6 -7*x^4 +14*x^2 -7 =0. - R. J. Mathar, Aug 29 2025

EXAMPLE

0.8677674782351162409515366656967175092199814555749197528890946...