|
%I #14 Mar 21 2024 14:25:24
%S 1,0,3,5,2,7,6,1,8,0,4,1,0,0,8,3,0,4,9,3,9,5,5,9,5,3,5,0,4,9,6,1,9,3,
%T 3,1,3,3,9,6,2,7,5,6,0,5,2,7,9,7,2,2,0,5,5,2,5,6,0,1,2,8,2,9,2,6,0,2,
%U 2,7,8,9,8,9,9,5,2,0,7,9,8,7,6,8,9,4,7,1,8,9,8,7,7,6,9,9,8,6,6,2,0,8,3,5,8
%N Decimal expansion of secant of 15 degrees (cosecant of 75 degrees).
%C Side length of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link).
%C A quartic integer. - _Charles R Greathouse IV_, Aug 27 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EquilateralTriangle.html">Equilateral Triangle</a>.
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F a(n) = sec(Pi/12) = sec(A019679) = sqrt(6) - sqrt(2) = A010464-A002193 = csc(5*Pi/12) = 1/sin(5*Pi/12) = 1/sin(10*A019691) = 1/A019884.
%F Equals Product_{k >= 1} 1/(1 - 1/(36*(2*k - 1)^2)). - __Antonio Graciá Llorente_, Mar 20 2024
%e 1.03527618041008304939559535049...
%t RealDigits[Sec[15 Degree],10,120][[1]] (* _Harvey P. Dale_, Jun 03 2015 *)
%o (PARI) sqrt(6) - sqrt(2) \\ _Charles R Greathouse IV_, Aug 27 2017
%Y Cf. A019679, A019691, A019884, A010464, A002193.
%K cons,nonn
%O 1,3
%A _Rick L. Shepherd_, Jun 24 2006
|
