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Decimal expansion of tangent of 36 degrees.
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%I #53 Nov 23 2024 05:50:57

%S 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 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 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 Decimal expansion of tangent of 36 degrees.

%C Also the decimal expansion of cotangent of 54 degrees. - _Mohammad K. Azarian_, Jun 30 2013

%C A quartic integer. - _Charles R Greathouse IV_, Aug 27 2017

%H Ivan Panchenko, <a href="/A019934/b019934.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

%F This number is sqrt(5-2*sqrt(5)). This number * A019970 = sqrt(5) = A002163. - _R. J. Mathar_, Jun 18 2006

%F The smallest positive solution of cos(4*arctan(x)) = cos(6*arctan(x)). - _Thomas Olson_, Oct 03 2014

%F 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 Equals Product_{k>=1} (1 + (-1)^k/A063226(k)). - _Amiram Eldar_, Nov 23 2024

%F Equals 1/A019952. - _Hugo Pfoertner_, Nov 23 2024

%e 0.72654252800536088589546675748061874961609239296520...

%t RealDigits[Tan[36 Degree],10,120][[1]] (* _Harvey P. Dale_, Nov 06 2012 *)

%o (PARI) tan(Pi/5) \\ _Charles R Greathouse IV_, Aug 27 2017

%Y Cf. A019934, A019952, A019970, A002163, A063226.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_