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A272490
Decimal expansion of the edge length of a regular 13-gon with unit circumradius.
7
4, 7, 8, 6, 3, 1, 3, 2, 8, 5, 7, 5, 1, 1, 5, 5, 3, 4, 2, 9, 7, 5, 0, 7, 4, 5, 2, 5, 2, 0, 4, 2, 3, 7, 9, 0, 4, 0, 6, 3, 4, 6, 0, 4, 5, 4, 7, 6, 6, 1, 2, 0, 2, 6, 7, 1, 0, 3, 1, 9, 4, 3, 7, 3, 2, 3, 6, 6, 3, 1, 2, 5, 7, 0, 1, 5, 0, 3, 7, 4, 3, 9, 2, 2, 3, 8, 9, 9, 6, 4, 4, 4, 1, 7, 2, 8, 8, 9, 4, 5, 1, 7, 9, 4, 6
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 = 13, and the constant, a = e(13), 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/13) = 2*cos(Pi*11/26).
EXAMPLE
0.47863132857511553429750745252042379040634604547661202671031943...
MATHEMATICA
RealDigits[N[2Sin[Pi/13], 100]][[1]] (* Robert Price, May 01 2016 *)
PROG
(PARI) 2*sin(Pi/13)
CROSSREFS
Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A255241 (n=14), A130880 (n=18), A272491 (n=19).
Sequence in context: A154687 A115021 A200367 * A261654 A332504 A121488
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 01 2016
STATUS
approved