I took a clear plastic tube and attached two circle protractors that could be rotated up and down the tube.

At that time of year the winter solstice was coming, and the Sun was moving into a lower declination in the sky. 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. These angles (55.6° and 34.4°) are the golden section of 90°.

I needed a way to measure and compare the amount of sunlight collected by the pattern.

This recorded the voltage that each model made over a period of time. "People see winter as a cold and gloomy time in nature. The amazing thing is that the mathematical fractions were the same numbers as the Fibonacci sequence!

I started my measurements in October and tested my models through December. The Secret of the Fibonacci Sequence in Trees main content. Fibonacci used patterns in ancient Sanskrit poetry from India to make a sequence of numbers starting with zero (0) and one (1). And, of course, we need a node for the root.If we look at the left subtree and the right subtree for long enough, we’ll notice that they seem familiar. But the most interesting results were in December, when the Sun was at its lowest point in the sky. https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

(Livio)In 1754, a naturalist named Charles Bonnet observed that plants sprout branches and leaves in a pattern, called phyllotaxis.

Why are there different Fibonacci patterns among trees? Lakes and ponds freeze, and animals scurry to burrows to wait for spring.

I am testing different Fibonacci patterns now.

Count the clockwise and counterclockwise spirals that reach the outer edge, and you’ll usually find a pair of numbers from the sequence: 34 and 55, or 55 and 89, or — with very large sunflowers — 89 and 144.

Pine Cones.

Evolution chose the Fibonacci pattern to help trees track the Sun moving in the sky and to collect the most sunlight even in the thickest forest.I saw patterns that showed that the tree design avoided the problem of shade from other objects. I had the next mystery to solve. Electricity dropped in the flat-panel array when shade fell on it.

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?

It even looks nicer because it looks like a tree.