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A272491 Decimal expansion of the edge length of a regular 19-gon with unit circumradius. 8
3, 2, 9, 1, 8, 9, 1, 8, 0, 5, 6, 1, 4, 6, 7, 7, 8, 8, 2, 8, 7, 3, 0, 4, 1, 1, 8, 1, 7, 5, 8, 7, 6, 8, 3, 9, 0, 2, 4, 3, 4, 4, 9, 6, 6, 7, 1, 9, 3, 0, 8, 2, 4, 6, 7, 0, 2, 9, 4, 2, 5, 4, 8, 0, 9, 8, 1, 5, 3, 8, 0, 5, 7, 0, 4, 9, 4, 3, 4, 1, 2, 5, 9, 5, 5, 7, 4, 6, 2, 8, 7, 6, 0, 1, 8, 7, 9, 8, 6, 0, 7, 7, 2, 8, 5 (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 = 19, and the constant, a = e(19), 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/19) = 2*cos(Pi*17/38).

EXAMPLE

0.32918918056146778828730411817587683902434496671930824670294254...

MATHEMATICA

RealDigits[N[2Sin[Pi/19], 100]][[1]] (* Robert Price, May 01 2016 *)

PROG

(PARI) 2*sin(Pi/19)

CROSSREFS

Cf. A004169, A019434.

Edge lengths of nonconstructible n-gons: A271487 (n=7), A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18).

Sequence in context: A211878 A060481 A228492 * A010271 A143074 A173624

Adjacent sequences:  A272488 A272489 A272490 * A272492 A272493 A272494

KEYWORD

nonn,cons,easy,changed

AUTHOR

Stanislav Sykora, May 01 2016

STATUS

approved

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Last modified May 23 06:21 EDT 2017. Contains 286909 sequences.