

A272487


Decimal expansion of the edge length of a regular heptagon with unit circumradius.


3



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
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OFFSET

0,1


COMMENTS

The edge length e(m) of a regular mgon 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).


EXAMPLE

0.8677674782351162409515366656967175092199814555749197528890946...


MATHEMATICA

N[2*Sin[Pi/7], 25] (* G. C. Greubel, May 01 2016 *)


PROG

(PARI) 2*sin(Pi/7)


CROSSREFS

Cf. A004169, A019434.
Edge lengths of nonconstructible ngons: 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
Adjacent sequences: A272484 A272485 A272486 * A272488 A272489 A272490


KEYWORD

nonn,cons,easy


AUTHOR

Stanislav Sykora, May 01 2016


STATUS

approved



