Curious nature: nature is a mathematician
Math is magic. It is the language of the universe in which most laws conform. Galileo said that “the book of nature is written in the language of mathematics”, and on November 23 we reflect on how a seemingly simple mathematical sequence connects us to something greater. Happy Fibonacci day!
A brief history to begin with. Many years ago we learned that Roman numerals were not the most efficient means of calculation and we switched to the Arabic numeral order we use today.
Once we had this new language of understanding, it didn’t take long before Italian-born Leonardo Bigollo Pisano, aka Fibonacci, discovered a hidden message from the world around us. Indian scholars of 1,300 years ago had realized this phenomenon before, but it was brought to the West in 1202 by the infamous Fibonnaci.
The Fibonacci sequence is an equation represented as such that each number is the sum of the previous two, starting from 0 and 1. So, 0+1=1,1+1=2, 1+2=3, 5, 8 , 13, 21, 34, and infinitely continuous.
If you take the numbers in the Fibonacci sequence, especially the larger ones, and divide one of them by the number before it in the sequence, you consistently get about 1.618…which the Greeks found out, called phi φ or the golden ratio. It’s an irrational number, which means we can’t write it as a simple fraction, but phi is as far from being a simple fraction as possible. We naturally get Fibonacci numbers when we use the golden ratio.
If you take a rectangle whose sides are successive Fibonacci numbers like the image below and draw an arc through each section, an infinite spiral develops.
This spiral, this golden ratio, phi, Fibonacci numbers are constantly found in the world around us. Why?
Simply put, nature knows this is the most effective and efficient way of organization. Imagine that you are a plant and want to capture as much sunlight and water as possible. If you grow in a straight line, you will jam the old leaves under you and they will die. They try to squeeze out as much growth potential as possible, ensuring that all of their leaves have the optimum opportunity to reach sunlight.
See this spiral pattern in the shell of the Coopers Rocky Mountain Snail. These shells are everywhere in the valley and not just near the water. See how the spiral starts out tight and slowly expands.
Even with snow covering the ground, the sequence can be seen in action. Get a bouquet of flowers for your loved ones. Count the petals on the flowers and if they have not been damaged, they are equal to a Fibonacci number.
These are just a few examples of the phenomena that surround us. Travel to the coast and you will see this spiral like an ocean wave. Travel above the troposphere and we see this spiral in hurricanes. Ascend light years into space and we see this spiral in our Milky Way galaxy. This phenomenon is not only all around us, it is within us. The proportions of our face, body and DNA exhibit elements of this efficient mathematical organization
With time and careful observation, we are able to uncover secrets and appreciate our connection to the universe. The next time you look at a pinecone, your hands, a sunflower, tree branches, or look at the night sky, remember Fibonacci and the magic of math in nature.
Tayler Branson is a naturalist at the Walking Mountains Science Center. You can find her taking a nature walk at WMSC to show Fibonacci in pine cones.