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 A255241 Decimal expansion of 2 cos(3 Pi/7). 9
 4, 4, 5, 0, 4, 1, 8, 6, 7, 9, 1, 2, 6, 2, 8, 8, 0, 8, 5, 7, 7, 8, 0, 5, 1, 2, 8, 9, 9, 3, 5, 8, 9, 5, 1, 8, 9, 3, 2, 7, 1, 1, 1, 3, 7, 5, 2, 9, 0, 8, 9, 9, 1, 0, 6, 2, 3, 9, 7, 4, 0, 3, 1, 7, 9, 4, 8, 4, 2, 4, 6, 4, 0, 5, 7, 0, 9, 4, 6, 3, 8, 1, 4, 9, 1, 6, 2, 1, 0, 5, 2, 1, 6, 1, 4, 5, 9, 1, 2, 6, 9, 7, 4, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is also the decimal expansion of 2*sin(Pi/14). rho_2 := 2*cos(3*Pi/7) and rho(7) := 2*cos(Pi/7) (see A160389) are the two positive zeros of the minimal polynomial C(7, x) = x^3 - x^2 - 2*x + 1 of the algebraic number rho(7), the length ratio of the smaller diagonal and the side in the regular 7-gon (heptagon). See A187360 and a link to the arXiv paper given there, eq. (20) for the zeros of C(n, x). The other zero is negative, rho_3 := 2*cos(5*Pi/n). See -A255249. Also the edge length of a regular 14-gon with unit circumradius. Such an m-gon is not constructible using a compass and a straightedge (see A004169). With an even m, in fact, it would be constructible only if the (m/2)-gon were constructible, which is not true in this case (see A272487). - Stanislav Sykora, May 01 2016 LINKS Stanislav Sykora, Table of n, a(n) for n = 0..2000 Wikipedia, Constructible number Wikipedia, Regular polygon FORMULA 2*cos(3*Pi/7) = 2*sin(Pi/14) = 0.4450418679... See A232736 for the decimal expansion of cos(3*Pi/7) = sin(Pi/14). EXAMPLE 0.445041867912628808577805128993589518932711137529089910623974031... MATHEMATICA RealDigits[N[2Cos[3Pi/7], 100]][[1]] (* Robert Price, May 01 2016 *) PROG (PARI) 2*sin(Pi/14) CROSSREFS Cf. A004169, A160389, A255249, A232736, A187360. Edge lengths of other nonconstructible n-gons: A271487 (n=7), A272488 (n=9), A272489 (n=11),A130880 (n=18), A272491 (n=19). - Stanislav Sykora, May 01 2016 Sequence in context: A111481 A111763 A159892 * A200694 A021696 A006581 Adjacent sequences:  A255238 A255239 A255240 * A255242 A255243 A255244 KEYWORD nonn,cons AUTHOR Wolfdieter Lang, Mar 13 2015 EXTENSIONS Offset corrected by Stanislav Sykora, May 01 2016 STATUS approved

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Last modified November 16 09:21 EST 2018. Contains 317268 sequences. (Running on oeis4.)