Golden angle

As its sine and cosine are transcendental numbers, the golden angle cannot be constructed using a straightedge and compass.

Let ƒ be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle.

But since it follows that This is equivalent to saying that φ 2 golden angles can fit in a circle.

[2] Analysis of the pattern shows that it is highly sensitive to the angle separating the individual primordia, with the Fibonacci angle giving the parastichy with optimal packing density.

[3] Mathematical modelling of a plausible physical mechanism for floret development has shown the pattern arising spontaneously from the solution of a nonlinear partial differential equation on a plane.

The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio
The angle between successive florets in some flowers is the golden angle.
Animation simulating the spawning of sunflower seeds from a central meristem where the next seed is oriented one golden angle away from the previous seed.