“Consider the lilies, how they grow: they neither toil nor spin; but I tell you, not even Solomon in all his glory clothed himself like one of these.” – Luke 12:27

Many different people have said it in many different ways: Math is the language of the universe. Depending on one’s view of mathematics, that’s either a profoundly inspiring or downright terrifying statement. If fourth period Algebra 2 class is the language of the universe, we may be perfectly fine being illiterate.

But if the sentiment is correct, what does that language sound like? Is it melodic and lilting, like Tolkien’s Elvish? Or more guttural and forceful, like Worf’s Klingon? And what does it look like? Is it flowing and artistic like Kanji or blockish and industrial like Cyrillic?

There are lots of different ways to answer those questions. Here’s one of them:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …

This list is the somewhat famous and definitely mysterious Fibonacci Series. If mathematics is indeed the language of the universe, this sequence of numbers can be thought of as a primary reader akin to the Dick and Jane books of old.

The pattern

If you don’t already know the pattern behind the Fibonacci numbers, look at the series above again and see if you can determine what ought to be the next number in the sequence. We’ll wait for you. What comes after 144?

…

Well? Did you get 233?

Fibonacci numbers are determined by adding the previous two numbers in the sequence. So the next number is found by adding 89 + 144.

Pretty mundane, right? Just a simple, recursive addition problem—what could possibly be the big deal?

The big deal is something not even Fibonacci himself could have predicted.

The man

The reason Leonardo of Pisa (aka “Fibonacci,” literally son of Bonaccio) could never have predicted the importance of the numbers named after him is that he had essentially nothing to do with the discovery of these numbers.

Leonardo of Pisa had a tremendous impact on mathematics. Based on his observations during his travels to the East, he introduced the decimal system and Arabic numerals to the Mediterranean area in the early 1200s. That’s a big deal! Roman numerals and a lack of place value were not going to lead Europe into an academic renaissance. Fibonacci was brilliant, and we should be thankful for his contributions; it’s just that the Fibonacci numbers weren’t really one of them. In his famous 1202 book Liber Abaci, in which he introduced Hindu-Arabic numerals to the West, he included a chapter of “word problems” (to borrow a modern term). In this chapter Leonardo included a single question about rabbits and their breeding habits (Spoiler alert: frequent). The answer to this question was the Fibonacci sequence. Somebody many centuries later made this connection and named the sequence after Fibonacci, heeding the time-honored tradition of naming mathematical and scientific discoveries after the first European male to mention them. But before, during, and after Fibonacci’s time, cultures have noticed Fibonacci numbers in nature and responded to the Fibonacci sequence in their mathematics, their writings, and their art. Fibonacci himself noted that he first observed the sequence in use in India. And the Indian mathematicians were just scratching the surface of how these numbers are seen in nature.

The botanical big deal

Why are four-leaf clovers considered lucky? Because four-leaf clovers are rare. Why are four-leaf clovers rare? Because almost all clovers have three leaves. This is the most elementary example of Fibonacci numbers at work in botany. It’s really difficult to find plants that have 4 petals or leaves. Most have 3 or 5. Or 13 (like the ragwort). Or 21 (like black-eyed susan). Or 34 (plantains). And while not all plants in those species have those exact numbers of petals in every example, they’re always very close and the average for that species is always the associated Fibonacci number.

It’s not just plant petals. The seed heads of daisies and sunflowers have swirling rows, and in the case of the sunflower there are 34 rows in one direction and 55 in the other. Those are oddly specific numbers, aren’t they? One might expect that for smaller plants it would be “easy” to land on a number like 3 and 5 with some regularity. But 55? 89? It starts to feel like there’s a purpose behind these numbers.

The fruit of plants also demonstrate a tendency towards Fibonacci numbers. Next time you’re in the produce section, pick up a pineapple. The large circular shapes on the rind of a pineapple run in diagonals. Count the “flattest” diagonals and you will see 5 rows. Count the next steepest, rising in the opposite direction, and there will be 8 rows. Count the diagonal that is almost vertical, and there will be 13 rows. And this is always true—this isn’t an average of all pineapples, with some below those numbers and some above. It’s true of every pineapple on this planet regardless of its point of origin. Pinecone scales spiral out from the stem in the same arrangement. Pineapples, with their tropical origin, and pinecones, from more temperate climates, are built the same way. They both use Fibonacci numbers. The same Fibonacci numbers in each case.

Trees demonstrate this tendency as well. Find a tree, and stand facing this tree so that directly in front of you is the location where a branch connects to the trunk. Look up or down the tree to find a second branch that comes out of the trunk in the same direction. Count the number of branches in between the two branches that you just found. It’ll be a Fibonacci number.

There are a number of other examples in botany; apples, cabbage, broccoli, cauliflower, bananas, and a variety of other species of flowers are all consistently Fibonacci-like in their growth patterns.

The benefits of being Fibonacci

What is the reason plants tend to grow according to this otherwise unremarkable pattern of numbers? Is there a demonstrated benefit?

Well…yes! Notice that all of these characteristics have to do with spiraling of some sort. The petals rotate around the daisy. The seed head of a sunflower has swirls of seeds. The scales of a pineapple revolve around its stem. The branches circle around the trunk of a tree.

It turns out that Fibonacci numbers maximize the efficiency of a spiral pattern. Let’s use the tree as an example: The purpose of leaves on a tree is to gather sunlight and convert it to chemical energy via photosynthesis. This obviously wouldn’t work if all the branches stuck out in the same direction. Upper branches would block lower ones from receiving sunlight, so it makes sense for the branches to emerge from the trunk in different directions. And it makes sense for the tree to accomplish this in a way that conserves as much of that converted energy as possible (the most efficient way). That route to maximum efficiency, according to scientists who study these kinds of things, uses the Fibonacci sequence of numbers.

Be thankful

God created plants with a mechanism in place to minimize the amount of work they have to do simply to remain alive. In point of fact, he gave them a mechanism that allows survival in the first place. When God called his creation “good” in Genesis, he didn’t just mean that it looked good. The systems he put in place to allow nature to thrive were also “good.” These systems get the job done.

God cared enough about his creation to build in systems that make even the lowest forms of life able to survive and thrive with maximum efficiency. What does this say about God’s care for us, whom he values more than the trees? Consider the lilies again.

Joel Bezaire earlier wrote on fractals and set theory for The Behemoth. This is the first article in a series on Fibonacci numbers in nature.

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