…
The branches seemed to have a spiral pattern that reached up into the sky. I had a hunch that the trees had a secret to tell about this shape. Investigating this secret led me on an expedition from the Catskill Mountains to the ancient Sanskrit poetry of India; from the 13th-century streets of Pisa, Italy, and a mysterious mathematical formula called the "divine number" to an 18th-century naturalist who saw this mathematical formula in nature; and, finally, to experimenting with the trees in my own backyard.
…
My investigation started with trying to understand the spiral pattern. I found the answer with a medieval mathematician and an 18th-century naturalist. In 1209 in Pisa, Leonardo of Pisano, also known as "Fibonacci," used his skills to answer a math puzzle about how fast rabbits could reproduce in pairs over a period of time. While counting his newborn rabbits, Fibonacci came up with a numerical sequence. Fibonacci used patterns in ancient Sanskrit poetry from India to make a sequence of numbers starting with zero (0) and one (1). Fibonacci added the last two numbers in the series together, and the sum became the next number in the sequence. The number sequence started to look like this: 1, 1, 2, 3, 5, 8, 13, 21, 34... . The number pattern had the formula Fn = Fn-1 + Fn-2 and became the Fibonacci sequence. But it seemed to have mystical powers! When the numbers in the sequence were put in ratios, the value of the ratio was the same as another number, φ, or "phi," which has a value of 1.618. The number "phi" is nicknamed the "divine number" (Posamentier). Scientists and naturalists have discovered the Fibonacci sequence appearing in many forms in nature, such as the shape of nautilus shells, the seeds of sunflowers, falcon flight patterns and galaxies flying through space. What's more mysterious is that the "divine" number equals your height divided by the height of your torso, and even weirder, the ratio of female bees to male bees in a typical hive! (Livio)
…
I designed and built my own test model, copying the Fibonacci pattern of an oak tree. I studied my results with the compass tool and figured out the branch angles. The pattern was about 137 degrees and the Fibonacci sequence was 2/5. Then I built a model using this pattern from PVC tubing. In place of leaves, I used PV solar panels hooked up in series that produced up to 1/2 volt, so the peak output of the model was 5 volts. The entire design copied the pattern of an oak tree as closely as possible.
I needed to compare the tree design pattern's performance. I made a second model that was based on how man-made solar panel arrays are designed. The second model was a flat-panel array that was mounted at 45 degrees. It had the same type and number of PV solar panels as the tree design, and the same peak voltage. My idea was to track how much sunlight each model collected under the same conditions by watching how much voltage each model made.
…