UNION — Math and nature, as different as they may seem, walk hand in hand with each other. Math is the bare bones theory, and nature is that theory showcased in full color.
If that does not add up, before reading this article, go into the backyard or kitchen and find a plant. Google an image of a plant if the real thing is not readily available. It does not matter what kind, just one with a lot of little repeating parts. A whole pineapple is the best choice, with all its hexagons ringing the fruit walls. Pinecones work well, as do large sunflower heads.
In “math lingo,” the plant will demonstrate the Fibonacci sequence, a series of numbers that takes the previous two numbers in a sequence and adds them together to get the next number.
To illustrate, notice the repeating parts of the plant. There is a pattern there, that subtle set of spirals branching out of the base of the pinecone or arching through the center of the sunflower. Pick up any plant with multiple repeating parts and see that many even have multiple sets of spirals. Use tape or a marker to mark off all that can be seen. There will be three or four different sets.
Count those spirals. There are typically three, five, or eight spirals in a set. In larger plants, one will find 21 or 34 spirals per set. Those numbers are part of a special, mathematically defined set of numbers, called the Fibonacci sequence: 0 1 1 2 3 5 8 13 21. The pattern doesn’t stop at 21, it can go on forever. Just add the previous two numbers to get the next one: 2+3=5, 3+5=8, 5+8=13, and so on and so forth. The number of all the spirals in a set of spirals on a plant will almost always be a number on the Fibonacci sequence.
Even if one stumbles across a number that is not on the sequence — maybe on a pinecone there are four or seven spirals per set instead of a Fibonacci number — that just means they are part of a different set of numbers similar to the Fibonacci sequence.
Plant parts make spirals, and those spirals line up with special numerical sequences, usually the Fibonacci sequence, one might learn in calculus. But why do they make spirals? And why is everything so precise, completely mathematical and calculable? It is not magic or evidence that plants are super geniuses.
When plants have new growth, be it a leaf, seed or a pinecone scale, they almost always add that growth at about a 137.5 degree angle away from the previous new growth. This is because 137.5 degrees away is usually the area furthest from all the other leaves, seeds or pinecone scales the plant has already grown. This is the area that has the most growth hormone built up, and the area where there is the most space for new growth. As they continue to grow at this angle, these small plant parts naturally form spirals. Because 137.5 degrees is related — in a very complex way — to the Fibonacci sequence, the number of spirals that form will be a Fibonacci number.
In short, plants are simple organisms whose new growth occurs wherever the most space allows. It is just basic logic — there is space, fill the space, do not try to fill space that has already filled and grow where its easiest to grow. Because of certain laws of mathematics, when plants follow these rules, a pattern will form. And with that pattern, the spirals naturally arise that follow the Fibonacci sequence.
Plants have mastered a pattern that has taken numerous mathematicians, biologists and physicists thousands of years to understand and replicate. What humans can only struggle to comprehend, nature has perfected, flawlessly and effortlessly.
Catherine Garner is a recent graduate of The University of South Carolina Honors College with a degree in Biological Sciences. She is one of two summer interns working through the end of July at Piedmont Physic Garden.