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

%I A144982 #15 Aug 31 2025 10:10:41
%S A144982 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,
%T A144982 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,
%U A144982 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
%N A144982 Decimal expansion of cos(Pi/24) = cos(7.5 degrees).
%C A144982 Octic number of denominator 2 and minimal polynomial 256x^8 - 512x^6 + 320x^4 - 64x^2 + 1. - _Charles R Greathouse IV_, May 13 2019
%H A144982 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a>
%F A144982 sqrt(2*sqrt(2)+sqrt(3)+1)/2^(5/4) =sqrt(A010466+A090388)/A011027.
%F A144982 Equals 2F1(9/16,7/16;1/2;3/4) / 2 . - _R. J. Mathar_, Oct 27 2008
%F A144982 4*this^3 -3*this = A144981. - _R. J. Mathar_, Aug 29 2025
%F A144982 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
%e A144982 Equals 0.9914448613738104111445575269285628712777382744...
%p A144982 evalf( sqrt(2*sqrt(2)+sqrt(3)+1)/2^(5/4)) ;
%t A144982 RealDigits[ Sqrt[2 + Sqrt[2 + Sqrt[3]]]/2, 10, 105] // First (* _Jean-François Alcover_, Feb 20 2013 *)
%t A144982 RealDigits[Cos[Pi/24],10,120][[1]] (* _Harvey P. Dale_, Feb 11 2024 *)
%o A144982 (PARI) cos(Pi/24) \\ _Charles R Greathouse IV_, May 13 2019
%K A144982 cons,easy,nonn,changed
%O A144982 0,1
%A A144982 _R. J. Mathar_, Sep 28 2008