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A228787 Decimal expansion of 2*sin(Pi/17), the ratio side/R in the regular 17-gon inscribed in a circle of radius R. 7
3, 6, 7, 4, 9, 9, 0, 3, 5, 6, 3, 3, 1, 4, 0, 6, 6, 3, 1, 4, 8, 8, 1, 7, 6, 7, 9, 2, 4, 1, 4, 5, 5, 1, 6, 4, 9, 7, 8, 2, 7, 7, 0, 4, 7, 6, 8, 8, 9, 9, 8, 8, 1, 1, 7, 0, 1, 3, 0, 1, 7, 1, 5, 4, 9, 7, 8, 2, 9, 8, 5, 6, 5, 0, 6, 1, 0, 0, 3, 4, 6, 0, 6, 1, 2, 0, 2, 3, 9, 0, 2, 4, 2, 1, 4, 6, 0, 9, 7, 1, 8, 5, 9, 3, 5, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

s(17) := 2*sin(Pi/17) is an algebraic integer of degree 16 (over the rationals). Its minimal polynomial is 17 - 204*x^2 + 714*x^4 - 1122*x^6 + 935*x^8 - 442*x^10 + 119*x^12 - 17*x^14 + x^16. Its coefficients in the power basis of the algebraic number field Q(2*cos(Pi/34)) are  [0, -15, 0, 140, 0, -378, 0, 450, 0, -275, 0, 90, 0, -15, 0, 1] (see row l = 8 of A228785). The decimal expansion of 2*cos(Pi/34) is given in A228788.

The continued fraction expansion starts with  0; 2, 1, 2, 1, 1, 2, 2, 2, 1, 5, 1, 3, 2, 2, 2, 1, 1, 43, 3, 1, 5, 2, 17, 2, ...

Gauss' formula for cos(2*Pi/17), given in A210644, can be inserted into s(17) = sqrt(2*(1 - cos(2*Pi/17))).

Since 17 is a Fermat prime, this number is constructible and can be written as an expression containing just integers, the basic four arithmetic operations, and square roots. See A003401 for more details. - Stanislav Sykora, May 02 2016

LINKS

Table of n, a(n) for n=0..106.

Kival Ngaokrajang, Illustration of the ratio side/R in the regular 17-gon inscribed in a circle of radius R

FORMULA

s(17) = 2*sin(Pi/17) = 0.367499035633140663148817679...

Equals sqrt(34-2*sqrt(17)-2*sqrt(34-2*sqrt(17))-4*sqrt(17+3*sqrt(17)-sqrt(34-2*sqrt(17))-2*sqrt(34+2*sqrt(17))))/4. - Stanislav Sykora, May 02 2016

MATHEMATICA

RealDigits[2Sin[Pi/17], 10, 100][[1]] (* Alonso del Arte, Jan 01 2014 *)

PROG

(PARI) 2*sin(Pi/17) \\ Charles R Greathouse IV, Nov 12 2014

CROSSREFS

Cf. A003401, A019434, A210644, A228785, A228788.

Sequence in context: A098990 A162195 A117361 * A245220 A165952 A156648

Adjacent sequences:  A228784 A228785 A228786 * A228788 A228789 A228790

KEYWORD

nonn,cons

AUTHOR

Wolfdieter Lang, Oct 07 2013

EXTENSIONS

Offset corrected by Rick L. Shepherd, Jan 01 2014

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.