Does the number of leaves on a branch follow Fibonacci numbers from top to bottom? Or is there more to nature than I really see it.

This question came up after reading this article:

Aidan Dwyer took a hike through the trees last winter and took notice of patterns in the mangle of branches. His studies into how they branch in very specific ways lead him to a central guiding formula, the Fibonacci sequence.

13-Year-Old Makes Solar Power Breakthrough by Harnessing the Fibonacci Sequence

The kid in the above article states that he planted tiny solar panels in the form of a tree and it followed the Fibonacci series. But I really do not get the connection between the Fibonacci series and the tree structure as a whole.

  • 2
    There are many web-sites that repeat the assertion about Fibonacci numbers appearing in nature. IMO, however, it would be good to have a more educational reference that explains how simple rules that maximise the surface area of petals/branches/leaves lead to fibonacci sequences. I recall reading an excellent explanation, but have failed to find it. – Oddthinking Oct 18 '12 at 13:05
  • Thank you for editing. I though it question was lost for the initial down votes until now. – karsnen Oct 30 '12 at 13:52

Vi Hart (Wikipedia biography) has produce a three part series of videos describing this phenomenon, called Doodling in Math: Spirals, Fibonacci, and Being a Plant.

It explores the nature of spirals, Fibonacci and the patterns seen in plants.

The third part in the series describe how this phenomena can be explained with a simple model of growth hormone.

Now, this isn't a formal academic document, but Hart provides a follow-up video containing appropriate references. If the goal of a good Skeptics.SE answer is to popularise scientific results, while retaining rigour, Vi Hart achieves this goal better than I ever will, so I am happy to defer to these videos as an answer.

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Head over to this web page : Fibonacci Numbers and Nature

Look at the 'Leaf arrangements' sections . You can clearly see that the leave arrangements and the turn of leaves both follow Fibonacci sequence and also note the section 'Always Fibonacci? ' You will find that Nature is too unpredictable to always follow Fibonacci number.

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