A144981 Decimal expansion of cos(Pi/8) = cos(22.5 degrees).

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, 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, 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

Offset

0,1

Comments

Also the real part of i^(1/4). - Stanislav Sykora, Apr 25 2012

Width of a regular octagon of unit diameter. See Bingane and Audet. - Michel Marcus, Oct 04 2021

Minimal polynomal 8x^4 - 8x^2 + 1. - Charles R Greathouse IV, Oct 30 2023

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Christian Bingane and Charles Audet, The equilateral small octagon of maximal width, arXiv:2110.00036 [math.MG], 2021.

Wikipedia, Exact trigonometric constants.

Index entries for algebraic numbers, degree 4

Formula

Equals sqrt(2 + sqrt(2))/2 = sqrt(3.41421...)/2 = 1.8477759.../2.

Equals Hypergeometric2F1([11/16, 5/16], [1/2], 3/4) / 2. - R. J. Mathar, Oct 27 2008

Example

Equals 0.923879532511286756128183189396788286822416625863642486115097...

Maple

evalf(sqrt(2+sqrt(2))/2) ;

Mathematica

RealDigits[ Sqrt[2 + Sqrt[2]]/2, 10, 111][[1]] (* Or *) RealDigits[ Cos[Pi/8], 10, 111][[1]] (* Robert G. Wilson v *)

Prog

(PARI) cos(Pi/8) \\ Michel Marcus, Dec 15 2015
(SageMath) numerical_approx(sqrt(2+sqrt(2))/2, digits=120) # G. C. Greubel, Sep 04 2022

Crossrefs

Cf. A019863: cos(Pi/5); A010527: cos(Pi/6); A073052: cos(Pi/7); A019879: cos(Pi/9).

Sequence in context: A257959 A137197 A340826 * A215267 A248322 A248321

Adjacent sequences: A144978 A144979 A144980 * A144982 A144983 A144984

Keyword

cons,easy,nonn

Author

R. J. Mathar, Sep 28 2008

Status

approved