login
A272489
Decimal expansion of the edge length of a regular 11-gon with unit circumradius.
9
5, 6, 3, 4, 6, 5, 1, 1, 3, 6, 8, 2, 8, 5, 9, 3, 9, 5, 4, 2, 2, 8, 3, 5, 8, 3, 0, 6, 9, 3, 2, 3, 3, 7, 9, 8, 0, 7, 1, 5, 5, 5, 7, 9, 7, 9, 4, 6, 5, 3, 3, 7, 4, 3, 6, 6, 2, 1, 6, 0, 6, 1, 2, 1, 7, 5, 6, 9, 7, 5, 9, 7, 0, 3, 8, 0, 5, 8, 3, 3, 6, 2, 4, 6, 9, 3, 5, 2, 3, 6, 9, 0, 3, 7, 7, 3, 0, 9, 9, 9, 3, 5, 9, 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 = 11, and the constant, a = e(11), 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).
FORMULA
Equals 2*sin(Pi/11) = 2*cos(Pi*9/22).
EXAMPLE
0.5634651136828593954228358306932337980715557979465337436621606121...
MATHEMATICA
RealDigits[N[2Sin[Pi/11], 100]][[1]] (* Robert Price, May 01 2016 *)
PROG
(PARI) 2*sin(Pi/11)
CROSSREFS
Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).
Sequence in context: A079267 A060296 A114598 * A259500 A274082 A199666
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 01 2016
STATUS
approved