A335605 Decimal expansion of arctan(log(phi)/(Pi/2)), the polar slope angle (in radians) of the golden spiral.

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, 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, 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

Offset

0,1

Comments

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)).

Links

Table of n, a(n) for n=0..103.

Wikipedia, Golden spiral.

Formula

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

Equals arctan(A212225). - Amiram Eldar, Jun 15 2020

Example

0.29727130470530517362994810317214622995424798032442...

Mathematica

RealDigits[ArcTan[2 * Log[GoldenRatio]/Pi], 10, 100][[1]] (* Amiram Eldar, Jun 15 2020 *)

Prog

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

Crossrefs

Cf. A000796, A001622, A002390, A212225.

Sequence in context: A357109 A011070 A230480 * A308320 A254140 A200991

Adjacent sequences: A335602 A335603 A335604 * A335606 A335607 A335608

Keyword

nonn,cons

Author

Stefano Occhetti, Jun 15 2020

Status

approved