# Where Botany meets Math and What is Cartesian vs Polar?

Simon did another coding challenge by Daniel Shiffman today, this time a short one called Phyllotaxis. You might be thinking, what in heaven’s name is Phyllotaxis? As it turned out, it’s the place where botany meets math! Phyllotaxis basically describes the arrangement of leaves in a plant, a repeating spiral that can be represented by a fraction describing the angle of windings leaf per leaf.

The numerator and denominator normally consist of a Fibonacci number and its second successor. The most famous example is the sunflower head. This phyllotactic pattern creates an optical effect of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals. These also turn out to be Fibonacci numbers. In some cases, the numbers appear to be multiples of Fibonacci numbers because the spirals consist of whorls. Phyllotactic patters are also closely related to the golden section in geometry.

The challenge Simon tried out today involved building an animation of a growing phyllotactic pattern.

After we shot the second video Simon corrected himself – he meant converting from Cartesian to Polar and not vice versa as he had said in the video. But what is Cartesian and Polar? And how exactly do you convert between them? We found a graphic explanation on Mathsisfun.com :