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
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
KEYWORD
AUTHOR
Stanislav Sykora, May 01 2016
STATUS
approved