~w00t~

The Young Naturalist Award, given to 13-year-old Aidan, who studied the Fibonacci sequence and applied it to trees, conjectured it made trees more efficient at capturing sunlight, and set off on a series of experiments and explorations:

Aidan studied leaf arrangments
Aidan measuring the spiral pattern

People see winter as a cold and gloomy time in nature. The days are short. Snow blankets the ground. Lakes and ponds freeze, and animals scurry to burrows to wait for spring. The rainbow of red, yellow and orange autumn leaves has been blown away by the wind turning trees into black skeletons that stretch bony fingers of branches into the sky. It seems like nature has disappeared.

But when I went on a winter hiking trip in the Catskill Mountains in New York, I noticed something strange about the shape of the tree branches. I thought trees were a mess of tangled branches, but I saw a pattern in the way the tree branches grew. I took photos of the branches on different types of trees, and the pattern became clearer.

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 asked the question of whether there is a secret formula in tree design and whether the purpose of the spiral pattern is to collect sunlight better. After doing research, I put together test tools, experiments and design models to investigate how trees collect sunlight. At the end of my research project, I put the pieces of this natural puzzle together, and I discovered the answer. But the best part was that I discovered a new way to increase the efficiency of solar panels at collecting sunlight!

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)

In 1754, a naturalist named Charles Bonnet observed that plants sprout branches and leaves in a pattern, called phyllotaxis. Bonnet saw that tree branches and leaves had a mathematical spiral pattern that could be shown as a fraction. The amazing thing is that the mathematical fractions were the same numbers as the Fibonacci sequence! On the oak tree, the Fibonacci fraction is 2/5, which means that the spiral takes five branches to spiral two times around the trunk to complete one pattern. Other trees with the Fibonacci leaf arrangement are the elm tree (1/2); the beech (1/3); the willow (3/8) and the almond tree (5/13) (Livio, Adler).

I now had my first piece of the puzzle but it did not answer the question, Why do trees have this pattern? I had the next mystery to solve. I designed experiments that attacked this question, but first I had to do field tests to understand the spiral pattern.

I built a test tool to measure the spiral pattern of different species of trees. I took a clear plastic tube and attached two circle protractors that could be rotated up and down the tube. When I put a test branch in the tube, I aligned the zero degree mark on one compass to match up with the first offshoot branch. I then moved and rotated the second compass up to the next branch spot. The second compass measured the angle between the two spots. I recorded the measurement and then moved up the branch step-by-step.

I collected samples of branches that fell to the ground from different trees, and I made measurements. My results confirmed that the Fibonacci sequence was behind the pattern.

But the question of why remained.

http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/aidan.html