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Feb 293 min read

How the Fibonacci Sequence Rules Our World

From the world’s largest skyscrapers to the most miniscule cells within our body, the omnipresence of mathematics in our world is nothing short of remarkable. Though often seen as an abstract discipline composed of arbitrary numbers and confined to textbooks, the Fibonacci Sequence serves as the underlying language that orchestrates the symphony of our natural world and fuels the innovation that propels our technological, societal, and personal advancements. 



Have you ever looked at a flower and noticed the striking spiral pattern at its center? This is a classic case of the Fibonacci sequence at work. Leonardo Fibonacci was an Italian mathematician from Pisa who discovered this crucial sequence of numbers. The sequence consists of ordered amounts where each number is the sum of its two preceding numbers. The first seven digits of the sequence are as follows: 1, 1, 2, 3, 5, 8, 13. This simple pattern is seen everywhere  from the leaves of a flower, to the branches of a tree, to the structure of our bones. A tree’s trunk will grow until it produces a branch, which then will produce another branch and so on; the Fibonacci sequence is seen when counting the number of branches on the tree section by section. Similarly, our bodies have 2 hands, both which have 5 fingers, and each finger is divided into 3 parts. When squaring each number and creating a grid-like pattern, a spiral forms. This spiral can be seen in shells, galaxies, waves, and much more. The numbers we see in nature are all Fibonacci numbers, all following the same extraordinary pattern.


When you take the Fibonacci sequence and manipulate it so that FN (your second term) is


divided by F_N-1 (your first term), it produces a ratio. As the Fibonacci sequence progresses, the limit of this ratio (what value this number approaches as you continue to infinitesimal amounts) reaches a special number called the Golden Ratio; 1.618 denoted by the Greek letter Phi (). This Golden Ratio is incredibly significant as it defines us. All faces, both human and non-human, follow the Golden Ratio. The mouth and nose are both positioned at ‘Golden’ sections of the distance between the eyes and the bottom of the chin. This proportion can also be seen in our side profiles, eyes, and ears. Though our faces are all different, the average facial proportion across all populations follows the Golden Ratio. In an ideal ‘smile’ (one commonly perceived as our societal standard of “beautiful”), the central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than the canines, and so on. Even in fruits and vegetables, the Golden Ratio emerges. In an artichoke, the leaves sprout at the stem every 137.5 degrees. This may seem like a random number, but is actually 360 degrees divided by the square of the Golden Ratio. In any fruit or vegetable that you can think of, the Golden Ratio will be present. 


Though you may dread your math class, don’t count mathematics out just yet. It’s much more than division and multiplication; it’s the very essence of reality. Mathematics is an indispensable tool that empowers us to comprehend, innovate, and navigate the complexities of our world. So next time you eat pineapple or paint your nails, try to notice the indistinguishable patterns given to you by mathematics and Mr. Fibonacci himself. 



 
Genevieve Dell Isola is a current senior from New Hampshire, currently attending boarding school in Rome, Italy. She is extremely passionate about mathematics and economics, and is looking to pursue a major in applied mathematics. In her free time, she loves exploring Rome and travelling around the world, as well as spending countless hours solving Sudokus and crossword puzzles. 






 


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