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A272489 Decimal expansion of the edge length of a regular 11-gon with unit circumradius. 8
5, 6, 3, 4, 6, 5, 1, 1, 3, 6, 8, 2, 8, 5, 9, 3, 9, 5, 4, 2, 2, 8, 3, 5, 8, 3, 0, 6, 9, 3, 2, 3, 3, 7, 9, 8, 0, 7, 1, 5, 5, 5, 7, 9, 7, 9, 4, 6, 5, 3, 3, 7, 4, 3, 6, 6, 2, 1, 6, 0, 6, 1, 2, 1, 7, 5, 6, 9, 7, 5, 9, 7, 0, 3, 8, 0, 5, 8, 3, 3, 6, 2, 4, 6, 9, 3, 5, 2, 3, 6, 9, 0, 3, 7, 7, 3, 0, 9, 9, 9, 3, 5, 9, 8, 8 (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 = 11, and the constant, a = e(11), 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/11) = 2*cos(Pi*9/22).

EXAMPLE

0.5634651136828593954228358306932337980715557979465337436621606121...

MATHEMATICA

RealDigits[N[2Sin[Pi/11], 100]][[1]] (* Robert Price, May 01 2016 *)

PROG

(PARI) 2*sin(Pi/11)

CROSSREFS

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A271487 (n=7), A272488 (n=9), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A079267 A060296 A114598 * A259500 A274082 A199666

Adjacent sequences:  A272486 A272487 A272488 * A272490 A272491 A272492

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, May 01 2016

STATUS

approved

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Last modified August 21 04:27 EDT 2017. Contains 290858 sequences.