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A272488
Decimal expansion of the edge length of a regular 9-gon with unit circumradius.
10
6, 8, 4, 0, 4, 0, 2, 8, 6, 6, 5, 1, 3, 3, 7, 4, 6, 6, 0, 8, 8, 1, 9, 9, 2, 2, 9, 3, 6, 4, 5, 1, 9, 1, 6, 1, 5, 2, 6, 1, 6, 6, 7, 3, 5, 0, 2, 8, 3, 2, 1, 2, 5, 6, 9, 3, 0, 0, 9, 6, 9, 9, 5, 3, 6, 9, 4, 2, 9, 5, 2, 7, 4, 0, 4, 1, 5, 5, 1, 9, 9, 1, 2, 8, 3, 8, 0, 3, 6, 4, 6, 7, 7, 0, 5, 1, 0, 9, 5, 0, 8, 0, 9, 4, 7
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 = 9, and the constant, a = e(9), 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/9) = 2*cos(Pi*7/18) = 2*A019829.
Equals Im((4+4*sqrt(3)*i)^(1/3)). - Gerry Martens, Mar 19 2024
EXAMPLE
0.6840402866513374660881992293645191615261667350283212569300969953...
MATHEMATICA
RealDigits[N[2Sin[Pi/9], 100]][[1]] (* Robert Price, May 01 2016 *)
PROG
(PARI) 2*sin(Pi/9)
CROSSREFS
Edge lengths of nonconstructible n-gons: A272487 (n=7), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).
Sequence in context: A184084 A346402 A255728 * A100608 A350795 A352769
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 01 2016
STATUS
approved