THE GOLDEN ANGLE

 

                        Given a circle divided into two sectors with larger arc, a, and smaller arc, b, in the golden ratio, the golden angle is the angle subtended by the smaller arc, b. The golden ratio is achieved by sectioning the circumference of a circle according to the golden section. The sectioning is done such that the ratio of the length of the larger arc, a, to the length of the smaller arc, b, is the same as the ratio of the full circumference, 2Πr, to the length of the larger arc, a.
Algebraically,
Let a+b be the circumference of the circle, divided into a longer arc of length 'a' and a smaller arc of length 'b' such that:

This implies that the golden angle is the angle subtended by arc b, it measures approximately: 

137.5077640500378546463487...°
 

The exact value of the golden angle is:

Where φ is the golden ratio.

Given the conditions above, Golden ratio,φ = a/b

The golden angle in nature is notably the angle separating the florets on a sunflower.