Finding Math in Nature

Written By: Hayeon Lee

Photograph Owned by iStock

When you are taking a walk outside or simply looking at the world around you, what is the first thing you notice? You might hear the melodic chirps of the birds or see the beautiful details of the colorful flowers. Though these observations themselves have vast importance, there are so many deeper layers of the natural world we know today. Mathematics plays an extremely fundamental role in our lives, far greater than the small parts we acknowledge. Notably, its key role in nature makes the field such a significant aspect of the growing understanding of the natural world around us. 

An important mathematical principle that is commonly associated with natural phenomena is the Fibonacci sequence. The Fibonacci sequence is a series of numbers where the next number is the sum of the two numbers before it. For example, if your first two numbers in the sequence is a 1, the next number would be the sum of the two 1’s and will be 2, and the next will be the sum of 1 and 2 to make 3, then the sum of 2 and 3 to make 5, and so forth. As interesting as this is, a more significant fact is how many aspects of nature adhere to this concept. The Fibonacci sequence can be seen in the number of spirals in a pine cone and of seeds in a sunflower. The leaves on stems are also frequently arranged in a pattern that corresponds to the Fibonacci numbers. There are so many great examples not mentioned here, and it is truly a very interesting topic to research and learn more about, due to how odd yet amazing the concept is. It goes to show how prevalent mathematics is in our daily lives, and how even the simple things can hold such intricacy.

Many of us have woken up in the morning to the chirping of the birds outside our windows. Though the songs and sounds of the birds may sometimes just sound annoying and repetitive, they actually have some mathematical qualities. In a study published in the Proceedings of the National Academy of Sciences, the researchers involved noticed how the notes of the hermit thrushes’ pitches had a direct correspondence to the harmonic series, which is where the musical tones are integer multiples of the baseline frequency. The harmonic series is deeply rooted in mathematical principles, as the ratios between the frequencies help construct the scales and intervals. Further research must be done in order to fully understand the relationship between bird songs and mathematics, but this breakthrough helps set an important foundation for future research and validates the predictions that there are, in fact, correlations between the two.

Lastly, another important part of the natural world is shapes. We are surrounded by shapes, though we rarely take the time to observe and notice them, as there are so many. Believe it or not, the shapes of certain features of nature play an important role in their efficiency and usefulness in studies. If you look closely at a honeycomb, you will notice that the holes are hexagons. Honeycombs are shaped like this not just for aesthetic purposes, but to maximize the amount of honey that can be stored in each cell while minimizing the amount of wax used around it. If you cut a tree, you will see the concentric circles within the trunk of a tree. These circular rings are crucial for understanding the natural world through a mathematical and scientific lens; the number of rings can tell us the age of the tree, and the width between the rings can offer insight to climate conditions in the past. Shapes, though they may seem insignificant since we are always surrounded by them, are ultimately a huge indicator of how breathtakingly and mathematically detailed nature can often be.

Overall, it is evident that mathematical concepts are seen and used more often than we expect, especially when it comes to nature. The correlation between math and nature is a beautiful thing, and it goes to show how everything in this world is connected in some way. Next time you are outside, take some time to truly see the features around you and how every piece of the world has its own story and splendor.