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.
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
KEYWORD
AUTHOR
R. J. Mathar, Sep 28 2008
STATUS
approved