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A272487
Decimal expansion of the edge length of a regular heptagon with unit circumradius.
10
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
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).
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
Cf. A160389.
Edge lengths of nonconstructible n-gons: A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).
Sequence in context: A182369 A104175 A019792 * A020828 A011465 A192409
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 01 2016
STATUS
approved