A210649 Decimal expansion of cos(Pi/17).

9, 8, 2, 9, 7, 3, 0, 9, 9, 6, 8, 3, 9, 0, 1, 7, 7, 8, 2, 8, 1, 9, 4, 8, 8, 4, 4, 8, 5, 5, 1, 9, 8, 7, 1, 6, 0, 9, 8, 7, 2, 2, 8, 7, 5, 0, 6, 5, 6, 3, 2, 8, 7, 5, 9, 9, 7, 3, 8, 0, 4, 5, 9, 2, 0, 3, 9, 0, 7, 8, 5, 2, 5, 5, 2, 2, 4, 4, 2, 1, 7, 4, 2, 9, 6, 8, 4

Offset: 0

Author

Bruno Berselli, Mar 27 2012

Keywords

• nonn
• cons

Comments

This algebraic number is related to the constructibility of the regular heptadecagon (see also A210644), it is a root of the polynomial 256*x^8-128*x^7-448*x^6+192*x^5+240*x^4-80*x^3-40*x^2+8*x+1.

The continued fraction expansion of cos(Pi/17) is 0, 1, 57, 1, 2, 1, 2, 2, 8, 9, 2, 3, 1, 1, 1, 1, 1, 2, 2, 13, 5, 1, 7, 84, 1, 1, 1,...

Expressed in terms of radicals, cos(Pi/17) is (1/8)*sqrt(2*(2*sqrt(sqrt((17/2)*(17-sqrt(17))) - sqrt((1/2)*(17-sqrt(17))) - 4*sqrt(2*(17+sqrt(17))) + 3*sqrt(17) + 17) + sqrt(17) + sqrt(2*(17-sqrt(17))) + 15)). - Jean-François Alcover, Dec 21 2012

Examples

			cos(Pi/17) = 0.9829730996839017782819488448551987160987228750656328...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Heptadecagon.
• Index entries for algebraic numbers, degree 8

Crossrefs

Cf. A019684, A210644.

Programs

Mathematica

RealDigits[Cos[Pi/17], 10, 87][[1]]

Maxima

fpprec:90; ev(bfloat(cos(%pi/17)));

PARI

cos(Pi/17)

Formula

Equals (i^(2/17) - i^(32/17))/2. - Peter Luschny, Apr 04 2020