Uncovering Hidden Sequences in Nature
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Uncovering Hidden Sequences in Nature

By Maya Inaltong

There are many beautiful patterns in mathematics, some of which can be observed outside a textbook and found in unexpected places in nature. 

One such famous pattern is The Fibonacci Sequence, which was first discovered over 2000 years ago by the ancient Indian poet and mathematician Acharya Pingala. Pingala came across the sequence when working with patterns in the classical language Sanskrit. However, the sequence got its name from Leonardo of Pisa, an Italian mathematician—later called Fibonacci—who introduced the sequence to the Western world. 

Each new term in the infinite Fibonacci Sequence is made from the sum of the two previous terms. The first ten terms of the sequence look like this: {0, 1, 1, 2, 3, 5, 8, 13, 21, 34} and these terms can be defined with the formula:

This sequence can be observed in many natural aspects of the universe. One famous example is the sunflower, where the sequence can be observed within its seeds. When counting the spirals of seeds in different directions, the spirals going in one direction add up to 21, the other direction 34, and the other direction 55, all numbers in the Fibonacci Sequence. Beyond sunflowers, this sequence can be observed in spiral leaf growth, pinecones, and many other plants.  

The sequence can be used to draw the Golden Spiral, a geometric pattern that is governed by the terms of the Fibonacci sequence. The spiral begins with two 1×1 squares that border a 2×2 square. Each square borders another square with the dimension of the sum of the two previous squares. So the next square would be a 3×3 square. And the next would be a 5×5 square, then an 8×8 square, and so on. 

The Fibonacci Sequence appears in many parts of the universe, from the seeds in sunflowers to the cells in organs and even in the formation of hurricanes and galaxies. The Golden Spiral is also a special tool for designers and artists, influencing many profound pieces of art and architecture such as Dali’s Sacrament of the Last Supper. 

The Fibonacci sequence can truly appear in the most unexpected places. The next time you observe a spiral or any aspect of nature, try to see if you can find the Fibonacci Sequence within it. You will be surprised at how many times you will find it!