The Magic of Fibonacci Numbers

“The Fibonacci numbers are Nature’s numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pine cone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.” —Nikhat Parveen, UGA

I’m kind of a nature nerd. I’ve been fascinated by the textures, colors and shapes in nature my entire life. I’ve taken thousands of photographs of flowers, bark, leaves and rocks, not to mention collecting baskets full of  rocks, seed pods, feathers, and small pieces of bark. I call my collected specimens my “Science Museum”. Started when I was a small child, my boys and I added to it when they were little, and I’ve continued adding to it, even today.

One of the things I find incredibly fascinating about nature is the Fibonacci sequence of numbers. In the seeming randomness of the natural world, we can find many instances of mathematical order involving the Fibonacci numbers. All we have to do is look around, starting in our own yards. For example, this begonia’s leaf arrangement, or phyllotaxis, around the stem is an awesome example of the Fibonacci numbers, or Golden Spiral, nature’s way of maximizing the space for each leaf and the average amount of light falling on each one. Fascinating, isn’t it?

When new leaves grow from a plant, they grow in a spiral around the plant’s stem. Nature spaces the leaves in this way so that higher leaves do not shade the lower leaves too much from sunlight. The number of turns in the spiral (from leaf to leaf) and the number of leaves that exist in the pattern in all cases express a Fibonacci fraction and therefore a Fibonacci ratio. The same pattern repeats again and again as the plant grows. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space. So nature isn’t trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect. The plant is responding to physical constraints, not to a mathematical rule.

The Fibonacci numbers are nature’s numbering system. They appear everywhere in nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pine cone, or the scales of a pineapple. Fibonacci numbers can also be seen in the arrangement of seeds on flower heads such as the sunflower. The seeds form spirals curving both to the left and the right, counting the spirals gives you two Fibonacci numbers, forming an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the center and not too sparse at the edges.

So, I’ve just been talking about plants, but Fibonacci characteristics can also be found in animals and people too! Mind boggling, right? I’ll bet you wish you’d paid better attention in math class now, right? I know I do!

Okay, enough about the magnificence of nature. I’ll leave you with this: math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds us that mathematics can be inspiring, too!)

Arthur Benjamin: The magic of Fibonacci numbers. This talk was presented at an official TED conference, 6/2013.