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A210649 Decimal expansion of cos(Pi/17).

%I A210649 #28 Feb 16 2025 08:33:17
%S A210649 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,
%T A210649 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,
%U A210649 7,8,5,2,5,5,2,2,4,4,2,1,7,4,2,9,6,8,4
%N A210649 Decimal expansion of cos(Pi/17).
%C A210649 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.
%C A210649 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,...
%C A210649 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
%H A210649 Vincenzo Librandi, <a href="/A210649/b210649.txt">Table of n, a(n) for n = 0..1000</a>
%H A210649 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Heptadecagon.html">Heptadecagon</a>.
%H A210649 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A210649 Equals (i^(2/17) - i^(32/17))/2. - _Peter Luschny_, Apr 04 2020
%e A210649 cos(Pi/17) = 0.9829730996839017782819488448551987160987228750656328...
%t A210649 RealDigits[Cos[Pi/17], 10, 87][[1]]
%o A210649 (PARI) cos(Pi/17)
%o A210649 (Maxima) fpprec:90; ev(bfloat(cos(%pi/17)));
%Y A210649 Cf. A019684, A210644.
%K A210649 nonn,cons
%O A210649 0,1
%A A210649 _Bruno Berselli_, Mar 27 2012