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# Mathematics in Nature: Cicadas and Beyond

## Mathematics in Nature: Cicadas and Beyond

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May 31, 2016
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With the emergence of 17-year periodical cicadas happening here in Cleveland Metroparks this year, a lot of cicada-related questions have come up. One of the questions, which is of particular interest to me, involves why the periodical cicada's life cycle is on such a strange, 17-year pattern. The answer to this question is even more interesting, as it involves properties of prime numbers. I won’t get into the details here because this topic was recently covered in another *Notes From the Field* blog (more information here), rather I would like to use this as a steppingstone to explore some of the intriguing ways in which mathematics and nature intertwine.

To begin, I would like to note that math and biology are very much connected, in fact, there are entire fields of study dedicated to exploring these connections. Computational biology, bioinformatics, and biophysics are all examples, and these fields have contributed to many great advances in our understanding of the natural world. However, the more we learn, the more questions we have, much like how one of the first questions we ask about cicadas once we hear about their 17-year cycle is, “why that number?”.

Plants often grow and arrange themselves according to mathematical patterns. For example, mature sunflowers and daisies have a peculiar arrangement for their florets, which amount to two sets of spirals that overlap. One set is made of clockwise spirals, the other counterclockwise spirals. If you count the number of spirals in each set and compare them, you will almost always find that they are consecutive numbers in a predictable sequence called the *Fibonacci sequence*. This famous sequence begins with 0 and 1, and continues by adding the previous two entries to get the next. For example, 0+1=1, so the first three numbers in the sequence are “0,1,1”. Then add 1+1 to get 2 as the next number, then 2+1 to get 3, etc. Here are the first 10 terms in the Fibonacci sequence: 0,1,1,2,3,5,8,13,21,34…