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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 (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 = 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).

LINKS

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

Wikipedia, Constructible number

Wikipedia, Regular polygon

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

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A271487 (n=7), A272488 (n=9), A272489 (n=11), A255241 (n=14), A130880 (n=18), A272491 (n=19).

Sequence in context: A154687 A115021 A200367 * A261654 A121488 A115291

Adjacent sequences:  A272487 A272488 A272489 * A272491 A272492 A272493

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, May 01 2016

STATUS

approved

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.