The Da Vinci Project

First of all, I had to understand what Fibonacci numbers are. I went to Wikipedia to get a definition. "In mathematics, the Fibonacci numbers form a sequence, one starts with 0 and 1, and then produces the next Fibonacci number by adding the two previous Fibonacci numbers. The first Fibonacci numbers for n = 0, 1, are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,..."  Then I had to see if these number occurred in Nature. Below are the steps I took to conduct the experiment to look for Fibonacci numbers in nature.

1. Flowers

• Collect a variety of different flowers
• Identify type of flower
• Count the number of petals on the flowers and check for Fibonacci spirals
• Photograph each
• Record findings on record sheet
• Find the number & percentage of flowers that have Fibonacci number sequences

2. Plants

• Collect a variety of different plants
• Identify plant
• If possible, count both the number of times around the stem, going from leaf to leaf, as well as count the leaves until encountering a leaf directly above the starting one
• Count the number of leaves
• Photograph them
• Record findings
• Find the number & percentage that have Fibonacci number sequences

3. Fruits & Vegetables

• Identify type of fruit or vegetable
• Count the number of petals, leaves, Fibonacci spirals, or leaf arrangement. If none exist, I had to get creative
• Count how many, if any, flat surfaces there are
• Cut in half and see if you can find any Fibonacci numbers
• Record on chart

Observations

1. 75% of the Flowers exhibited Fibonacci qualities
2. 81.8% of the Plants' petals or leaves exhibited Fibonacci qualities
3. 85% of the Vegetables & Fruits exhibited Fibonacci qualities
4. Neither Vines or Cacti had Fibonacci qualities

My hypothesis was proven correct. In fact, not only do we see the Fibonacci numbers more often than random, we see them more than 75% of the time. Some of the things I saw really surprised me, such as the pentagram that the apple's seeds were held in.

How does it work?

I did find the Fibonacci number happening more often than random because Nature has made these plants more efficient by gearing them towards Fibonacci numbers. Whether it gives the plant, flower, vegetable or fruit a way to get more sunlight, more room, or spread its seeds better, the Fibonacci numbers definitely help in Nature.

The reason why the Fibonacci numbers appear in nature varies based on which part of nature. For flowers, the reason that the number of petals and the way the spirals form are Fibonacci related is because it allows for optimal seed packing. For plants, the reason they have a Fibonacci number of leaves is that they can get the most sunlight. For fruits and vegetables, well, the same rule as plants. For further study I would like to study the Lucas Numbers.

The Lucas Numbers were invented by a man named Edouard Lucas. He was the man who gave the Fibonacci numbers their name and he discovered many of their connections to nature. However, he found out that the numbers that did not show qualities from the Fibonacci Numbers showed numbers from another series. This series, named the Lucas Numbers in Edouard Lucas's honor, goes 2, 1, 3, 4, 7, 11, 18, ... The Fibonacci rule of adding the latest two to get the next is kept, but here we start from 2 and 1 (in this order) instead of 0 and 1 for the (ordinary) Fibonacci numbers. I think the reason that some of the plants did not have the Fibonacci numbers is because one of them was a vine and one was a cactus. They both have other ways of getting energy.