Golden Angle

In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio.

The golden angle plays a significant role in the theory of phyllotaxis; for example, the golden angle is the angle separating the florets or branches on some plants or flowers (e.g. sunflower).

Plants have their leaves spread all around the stem to soak up as much sun as possible. Using the golden angle between two consecutive leaves is the most effective approach to spread the leaves around the stem.

Let’s see how this work:
Leaf 1:

Leaf 2: Would be at an angle of around 137.5° (The Golden Angle) from leaf 1

Leaf 3: Would be at an angle of around 137.5° (The Golden Angle) from leaf 2

And so on for all new leaves…

etc…

Python Challenge

For this challenge we will apply the golden angle to position the first 50 branches of a tree using Python Turtle:

Sunflower using Python Turtle and the Golden Angle