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A272488 Decimal expansion of the edge length of a regular 9-gon with unit circumradius. 8
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 (list; constant; graph; refs; listen; history; text; internal format)
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).

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Constructible number

Wikipedia, Regular polygon

FORMULA

Equals 2*sin(Pi/9) = 2*cos(Pi*7/18).

EXAMPLE

0.6840402866513374660881992293645191615261667350283212569300969953...

MATHEMATICA

RealDigits[N[2Sin[Pi/9], 100]][[1]] (* Robert Price, May 01 2016 *)

PROG

(PARI) 2*sin(Pi/9)

CROSSREFS

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A271487 (n=7), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A054042 A184084 A255728 * A100608 A234846 A244054

Adjacent sequences:  A272485 A272486 A272487 * A272489 A272490 A272491

KEYWORD

nonn,cons,easy,changed

AUTHOR

Stanislav Sykora, May 01 2016

STATUS

approved

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.