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A019934 Decimal expansion of tangent of 36 degrees.

%I A019934 #56 Aug 31 2025 13:04:08
%S A019934 7,2,6,5,4,2,5,2,8,0,0,5,3,6,0,8,8,5,8,9,5,4,6,6,7,5,7,4,8,0,6,1,8,7,
%T A019934 4,9,6,1,6,0,9,2,3,9,2,9,6,5,2,0,8,4,6,2,7,5,0,0,6,6,3,2,7,3,4,5,7,4,
%U A019934 9,3,9,1,8,4,5,6,8,3,0,8,8,4,2,0,5,7,7,5,2,2,2,1,6,1,4,0,0,9,1
%N A019934 Decimal expansion of tangent of 36 degrees.
%C A019934 Also the decimal expansion of cotangent of 54 degrees. - _Mohammad K. Azarian_, Jun 30 2013
%C A019934 A quartic integer. - _Charles R Greathouse IV_, Aug 27 2017
%H A019934 Ivan Panchenko, <a href="/A019934/b019934.txt">Table of n, a(n) for n = 0..1000</a>
%H A019934 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.
%H A019934 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A019934 This number is sqrt(5-2*sqrt(5)). This number * A019970 = sqrt(5) = A002163. - _R. J. Mathar_, Jun 18 2006
%F A019934 The smallest positive solution of cos(4*arctan(x)) = cos(6*arctan(x)). - _Thomas Olson_, Oct 03 2014
%F A019934 Let r(n) = (n - 1)/(n + 1) if n mod 4 = 1, (n + 1)/(n - 1) otherwise; then this constant (A019934) equals with Product_{n>=0} r(10*n+5) = (2/3) * (8/7) * (12/13) * (18/17) * ... - _Dimitris Valianatos_, Sep 14 2019
%F A019934 Equals Product_{k>=1} (1 + (-1)^k/A063226(k)). - _Amiram Eldar_, Nov 23 2024
%F A019934 Equals 1/A019952. - _Hugo Pfoertner_, Nov 23 2024
%F A019934 tan(Pi/5) = A019845 / A019863. - _R. J. Mathar_, Aug 31 2025
%F A019934 Smallest positive of the 4 real-valued roots of x^4-10*x^2+5=0. (Other A019970). - _R. J. Mathar_, Aug 31 2025
%e A019934 0.72654252800536088589546675748061874961609239296520...
%t A019934 RealDigits[Tan[36 Degree],10,120][[1]] (* _Harvey P. Dale_, Nov 06 2012 *)
%o A019934 (PARI) tan(Pi/5) \\ _Charles R Greathouse IV_, Aug 27 2017
%Y A019934 Cf. A019934, A019952, A019970, A002163, A063226.
%K A019934 nonn,cons,changed
%O A019934 0,1
%A A019934 _N. J. A. Sloane_