By Nikita Handel, Year 12
When I first learnt about Fibonacci numbers, I thought they were extremely dull (sorry Dr Barker). But over time, I’ve realised that they are actually quite special.
The Fibonacci numbers are a sequence where the first two terms are 0 and 1. After this, to get the next term you take the sum of the last two. So, the third term is 0+1=1 and the fourth term is 1+1=2. You eventually get a pattern of numbers which goes like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
I admit, this looks pretty unimpressive. But the interesting part comes when you look at the ratio of successive terms. This means that you take the fraction of a term over the previous term. For example, 13/8 or 34/21. As the Fibonacci numbers get bigger (and the sequence tends to infinity), we see a pattern forming. All these fractions are approximately 1.618. This number is known as the Golden Ratio, or phi.
The Golden Ratio crops up almost everywhere in nature. It feels odd that nature and maths are related, but it seems that even trees can’t get away from the quadratic formula. The Golden Ratio acts as a hidden rulebook for most species. It dictates the number of petals a flower can have; next time you see some flowers, you might spot that the number of petals is always a Fibonacci number. The Golden Ratio is also present in DNA molecules, which measure 34 angstroms long by 21 angstroms wide, both of which are Fibonacci numbers.
There is no complete understanding of why Fibonacci numbers appear in nature. A simple explanation is that species have evolved to use the Golden Ratio, as it seems to allow plants and animals to survive best. Some mathematicians even believe that human attractiveness is based on whether your face has Fibonacci proportions (young Leo DiCaprio is both visually and mathematically pleasing).
I think it’s rather humbling to realise the workings of nature are something we will never fully understand. It also puts a perspective on all those GCSE maths lessons- we somehow see applications of maths every day, without even realising it. My favourite application of the Fibonacci sequence is a Roman Cauliflower, which is an example of a natural fractal (a never-ending pattern). The number of spirals on each head is a Fibonacci number. While beautiful, they are also delicious (and grown in Jersey!).
So next time you're bored in a maths lesson, I recommend looking outside and remembering the bigger picture of nature, and how beautifully mathematical it is.
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