The other day I was lying at the base of a tree, my eyes travelling up the line of trunk up till where the branches perpendicularly fought against the anti-gravitational growth of their producer. As I observed the direction of the branches, I was reminded of the beautiful phenomenon that is the fibonacci sequence. The fibonacci sequence is one of these fantastic collisions of mathematics and biology, and is so beautiful and prevalent around us that I thought I’d just remind you all of it.
Although always present in nature, it was first acknowledged by 11th century Italian mathematician, Leonardo Pisano. He wondered how many rabbits could a single rabbit produce given optimal conditions. The results are the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, etc… where every number is the sum of the two prior to that. This came to be known as the Fibonacci sequence. When put in ratio, these numbers had a value of 1.618, also known as the ‘divine number’ or ‘golden ratio’.
The numbers can also be expressed in the following pattern, which as you can see strongly resembles a nautilus sea shell.
Other examples include the pistils in flower centres, many different types of flower petals, pinecone seeds, a dangling Monarch about to form a chrysalis, the shape of an egg, even the curve of your own ear! As well as the physical curve being plentifully represented, the golden ratio is also very common, for example your height divided by the hight of your torso.
The neat thing about trees is that both curve and ratio is represented. The branches sprout out in a spiral from the trunk (for example the almond tree in which it takes 8 branches to spiral 3 times around, a fibonacci ratio of 3/8). Not only this but if you look directly up a trunk, you can make out a distinctive anti-spiral curve of the individual branches originating at the trunk and curving around the tree. The advantage of this pattern in trees is the efficiency of sunlight access for photosynthesis. (I’d just like to note that not all trees follow this pattern, not all species have this anticlockwise curve)
so next time you’re strolling amongst trees, on a beach, breeding rabbits (I guess??), or by a flower garden, I encourage you to look with an observant eye for this beautiful pattern in nature.
Science Scholars 2019 