# The Secret of the Fibonacci Sequence in Trees

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Fibonacci in Trees

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.

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The Fibonacci tree design performed better than the flat-panel model. The tree design made 20% more electricity and collected 2 1/2 more hours of sunlight during the day. But the most interesting results were in December, when the Sun was at its lowest point in the sky. The tree design made 50% more electricity, and the collection time of sunlight was up to 50% longer!

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Interesting but not new. I heard and thought about this as a kid (decades ago). Google up "phyllotaxis and fibonacci" for example (e.g. http://www.sccs.swarthmore.edu/users/08/bb.../mitchison.pdf). What surprises me is that people think it *is* new.

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Interesting but not new. I heard and thought about this as a kid (decades ago). Google up "phyllotaxis and fibonacci" for example (e.g. http://www.sccs.swarthmore.edu/users/08/bb.../mitchison.pdf). What surprises me is that people think it *is* new.

Why would you be surprised that someone finds it new? I never heard of this and it is certainly new to me as it was to others that I emailed. If you noticed in the article, it was written by a 13 year old. It may not be new to you, but to him it certainly is.

There are also 4 petalled flowers:

and 6 petalled flowers:

So not everything fits the series. So what point are you making?

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The hyperlink picked up the right parenthese previously. This is a paper from 1977 and the observation is older than that:

http://www.sccs.swarthmore.edu/users/08/bb...s/mitchison.pdf

I thought my point was obvious. I have seen this story in different places, all implying that this is a novel discovery. That he apparently independently found this pattern is impressive, as is using it technologically, but it should not be touted as a brand new idea.

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The hyperlink picked up the right parenthese previously. This is a paper from 1977 and the observation is older than that:

http://www.sccs.swarthmore.edu/users/08/bb...s/mitchison.pdf

I thought my point was obvious. I have seen this story in different places, all implying that this is a novel discovery. That he apparently independently found this pattern is impressive, as is using it technologically, but it should not be touted as a brand new idea.

QFT. A book now published by Dover has a chapter on the logarithmic spiral which is a Fibonacci derivative. It summarizes the prior centuries work on the subject. This book was published in 1949, over 62 years ago talking about work done in the previous century.

ruveyn