%I #43 Oct 30 2023 02:15:59
%S 9,2,3,8,7,9,5,3,2,5,1,1,2,8,6,7,5,6,1,2,8,1,8,3,1,8,9,3,9,6,7,8,8,2,
%T 8,6,8,2,2,4,1,6,6,2,5,8,6,3,6,4,2,4,8,6,1,1,5,0,9,7,7,3,1,2,8,0,5,3,
%U 5,0,0,7,5,0,1,1,0,2,3,5,8,7,1,4,8,3,9,9,3,4,8,5,0,3,4,4,5,9,6,0,9,7,9,6,3
%N Decimal expansion of cos(Pi/8) = cos(22.5 degrees).
%C Also the real part of i^(1/4). - _Stanislav Sykora_, Apr 25 2012
%C Width of a regular octagon of unit diameter. See Bingane and Audet. - _Michel Marcus_, Oct 04 2021
%C Minimal polynomal 8x^4 - 8x^2 + 1. - _Charles R Greathouse IV_, Oct 30 2023
%H G. C. Greubel, <a href="/A144981/b144981.txt">Table of n, a(n) for n = 0..10000</a>
%H Christian Bingane and Charles Audet, <a href="https://arxiv.org/abs/2110.00036">The equilateral small octagon of maximal width</a>, arXiv:2110.00036 [math.MG], 2021.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Equals sqrt(2 + sqrt(2))/2 = sqrt(3.41421...)/2 = 1.8477759.../2.
%F Equals Hypergeometric2F1([11/16, 5/16], [1/2], 3/4) / 2. - _R. J. Mathar_, Oct 27 2008
%e Equals 0.923879532511286756128183189396788286822416625863642486115097...
%p evalf(sqrt(2+sqrt(2))/2) ;
%t RealDigits[ Sqrt[2 + Sqrt[2]]/2, 10, 111][[1]] (* Or *) RealDigits[ Cos[Pi/8], 10, 111][[1]] (* _Robert G. Wilson v_ *)
%o (PARI) cos(Pi/8) \\ _Michel Marcus_, Dec 15 2015
%o (SageMath) numerical_approx(sqrt(2+sqrt(2))/2, digits=120) # _G. C. Greubel_, Sep 04 2022
%Y Cf. A019863: cos(Pi/5); A010527: cos(Pi/6); A073052: cos(Pi/7); A019879: cos(Pi/9).
%K cons,easy,nonn
%O 0,1
%A _R. J. Mathar_, Sep 28 2008