1 1 2 3 5 8 13 21 34 55…
A keen observer would note that each number in the above sequence is the sum of the two numbers before it. These are known as Fibonacci numbers and are among the most famous number sequences in mathematics.
It is famous because of some unique properties. For example, every third number is even, every xth number is the multiple of Fx (e.g. 4th number = 3, 8th number = 21…) and the list goes on. It is also known to approximate golden spirals, a mathematical function that is closely related with yet another famous number: the golden ratio.
However, a more interesting (and more relatable) fact about these numbers is that they appear repeatedly in nature. It has been noted for many centuries that plants tend to follow the Fibonacci sequence in various ways. This includes the number of branches of trees that grow per year, the number of petals on a flower (almost all flowers have a Fibonacci number of petals) and most interesting of all: the arrangement of florets on the face of a sunflower. If one carefully scrutinises the face of a sunflower (also applies to pine cones), they will note that the florets (tiny pieces on the face) are arranged in what appears to be spirals. They are actually arranged on a stack of spirals, both clockwise and anti-clockwise. The number of spirals for both directions are always two Fibonacci numbers next to each other (e.g. 34 and 55).
This is because natural selection pushes the plants to arrange their florets, petals and tree branches in the most efficient manner possible, which is provided by the Fibonacci sequence.