A144982 Decimal expansion of cos(Pi/24) = cos(7.5 degrees).

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

Offset: 0

Author

R. J. Mathar, Sep 28 2008

Keywords

• cons
• easy
• nonn
• changed

Comments

Octic number of denominator 2 and minimal polynomial 256x^8 - 512x^6 + 320x^4 - 64x^2 + 1. - Charles R Greathouse IV, May 13 2019

Examples

			Equals 0.9914448613738104111445575269285628712777382744...
		

Links

• Index entries for algebraic numbers, degree 8

Programs

Maple

evalf( sqrt(2*sqrt(2)+sqrt(3)+1)/2^(5/4)) ;

Mathematica

RealDigits[ Sqrt[2 + Sqrt[2 + Sqrt[3]]]/2, 10, 105] // First (* Jean-François Alcover, Feb 20 2013 *)
RealDigits[Cos[Pi/24],10,120][[1]] (* Harvey P. Dale, Feb 11 2024 *)

PARI

cos(Pi/24) \\ Charles R Greathouse IV, May 13 2019

Formula

sqrt(2*sqrt(2)+sqrt(3)+1)/2^(5/4) =sqrt(A010466+A090388)/A011027.

Equals 2F1(9/16,7/16;1/2;3/4) / 2 . - R. J. Mathar, Oct 27 2008

4*this^3 -3*this = A144981. - R. J. Mathar, Aug 29 2025

Equals 2F1(-1/16,1/16;1/2;3/4) = 2F1(-1/12,1/12;1/2;1/2). - R. J. Mathar, Aug 31 2025