All 13th century mathematician Leonardo of Pisa wanted to do was calculate the growth of rabbit populations in a defined area.
What he ended up with was a formula that numerically explains patterns found in everything from spiral galaxies to planning the perfect Maine garden.
Known as the Fibonacci sequence, after Leonardo’s nickname, it’s a group of numbers starting at zero and stretching into infinity with each number equaling the sum of the two behind it.
You are surrounded by Fibonacci sequences all day, every day. Once you are aware of them, they are hard to miss. Slice open a cabbage from the garden, look at the population of your beehive or watch the development of a hurricane like the one currently churning up the East Coast.
Beyond its occurrence in nature, the sequence is used by painters, sewers, photographers and other artists in their creative projects.
A big part of the attraction has to do with the “the golden ratio.” It’s a formula calculated using the Fibonnaci sequence to create the perfect and most visually pleasing rectangle.
It’s not clear why people are most attracted to golden ratio rectangles, but scientists think it could be because its proportion — especially when the horizontal side is longer — is the easiest for the human eye to scan and process.
The exact ratio is 1:1.618, and it was used thousands of years ago in building the pyramids of egypt.
It’s also seen in concentric circles that spiral outward like the clouds swirling around the eye of Hurricane Lee or in that pinecone you found in the forest.
“It has to do to some extent with how things replicate in nature,” Brandon Hanson, PhD, assistant professor of mathematics at University of Maine. “The patterns look nice so we use them as a frame of reference [and] that’s the reason it shows up in manmade designs.”
Closer to home, the Fibonacci sequence can be used to plan and design a rectangular golden-ratio garden with different plants growing in each of the rectangular spaces.
Start by measuring the long sides of your rectangular garden spaces and then multiply that by .618. That will give you a length for the short sides for the most visually pleasing rectangular space for your plants. It’s also why the most popular garden bed size is 5-feet by 8-feet.
When it comes to planting your flowers or vegetables in that space, use the sequence to determine how many to put in your golden-ratio rectangle garden. That means you are going to plant in groupings of 1, 2, 3, 5, 8 and upward by adding together the last two numbers.
Some gardening catalogs have done the math for you by packaging flower bulbs in groups in accordance with the sequence.
For a purely mathematical garden, the formula has been used to figure out that the most visually appealing ratio for plants of different heights grouped together is one 6-foot plant or tree to three 4-foot shrubs or plants to eight two-and-a-half-foot plants.
Even though it was named for him, Fibonacci was not the first person to observe or use the sequence, Hanson said. More than 1,200 years before the Italian man described them, the numbers appeared in patterns in Sanskrit poetry.
“The sequence has certainly been around longer than Fibonacci,” Hanson said. “The reason why we think this is appealing is pretty subjective, but people have been mystified and excited by the Fibonacci sequence and golden ratio for a very long time.”