A335605 - OEIS

%I #44 Jul 01 2020 12:59:26

%S 2,9,7,2,7,1,3,0,4,7,0,5,3,0,5,1,7,3,6,2,9,9,4,8,1,0,3,1,7,2,1,4,6,2,

%T 2,9,9,5,4,2,4,7,9,8,0,3,2,4,4,2,3,9,5,1,2,6,0,2,5,8,3,1,4,0,3,1,2,7,

%U 9,8,8,3,7,8,2,9,9,9,4,3,7,8,7,9,6,6,1,8,5,2,1,9,2,4,5,7,2,2,9,5,0,2,4,1

%N Decimal expansion of arctan(log(phi)/(Pi/2)), the polar slope angle (in radians) of the golden spiral.

%C In the polar equation for a logarithmic spiral: r = a*e^(b*theta), b represents the tangent of angle alpha, where alpha is the polar slope of the curve. In a golden spiral equation, b = log(phi)/(Pi/2) (being: log the natural logarithm; phi the golden ratio: 1.61803398..., therefore, alpha = arctan(log(phi)/(Pi/2)).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_spiral#Polar_slope">Golden spiral</a>.

%F alpha = arctan(log(phi)/(Pi/2)).

%F Equals arctan(A212225). - _Amiram Eldar_, Jun 15 2020

%e 0.29727130470530517362994810317214622995424798032442...

%t RealDigits[ArcTan[2 * Log[GoldenRatio]/Pi], 10, 100][[1]] (* _Amiram Eldar_, Jun 15 2020 *)

%o (PARI) atan(log(((1+sqrt(5))/2))/(Pi/2))

%Y Cf. A000796, A001622, A002390, A212225.

%K nonn,cons

%O 0,1

%A _Stefano Occhetti_, Jun 15 2020