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A195707 Decimal expansion of arctan(sqrt(5/8)).

%I A195707 #17 Nov 20 2024 23:44:47
%S A195707 6,6,8,9,6,4,0,7,4,2,6,8,4,0,7,1,3,0,1,4,1,3,2,7,1,1,2,6,1,2,1,7,6,4,
%T A195707 7,8,0,1,6,9,3,0,7,1,8,1,1,9,6,3,4,7,0,8,1,6,2,9,2,9,7,6,0,3,5,2,0,5,
%U A195707 0,4,1,5,4,9,0,1,8,2,2,3,8,8,0,5,9,8,6,4,2,4,0,2,1,7,7,4,0,4,3,1
%N A195707 Decimal expansion of arctan(sqrt(5/8)).
%H A195707 G. C. Greubel, <a href="/A195707/b195707.txt">Table of n, a(n) for n = 0..10000</a>
%H A195707 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195707 Equals arcsin(sqrt(5/13)) = arccos(2*sqrt(2/13)). - _Amiram Eldar_, Jul 08 2023
%e A195707 arctan(sqrt(5/8)) = 0.6689640742...
%t A195707 r = Sqrt[5/8];
%t A195707 N[ArcSin[r], 100]
%t A195707 RealDigits[%]  (* A195703 *)
%t A195707 N[ArcCos[r], 100]
%t A195707 RealDigits[%]  (* A195700 *)
%t A195707 N[ArcTan[r], 100]
%t A195707 RealDigits[%]  (* A195707 *)
%t A195707 N[ArcCos[-r], 100]
%t A195707 RealDigits[%]  (* A195711 *)
%o A195707 (PARI) atan(sqrt(5/8)) \\ _G. C. Greubel_, Aug 19 2018
%o A195707 (Magma) SetDefaultRealField(RealField(100)); Arctan(Sqrt(5/8)); // _G. C. Greubel_, Aug 19 2018
%Y A195707 Cf. A195700, A195703, A195711.
%K A195707 nonn,cons
%O A195707 0,1
%A A195707 _Clark Kimberling_, Sep 23 2011