## Monday, 16 April 2012

### Phyllotaxis and shade

Have you ever wondered why you can get such good shade under some trees in summer? Gum trees are less shady because their leaves hang down on edge, avoiding the hot sun, but other plants arrange their leaves to catch as much sun as possible. When they do, a remarkable mathematical pattern emerges, and once again, it often involves the Fibonacci series.

Now we have had a mad fad for The Da Vinci Code, I probably don't need to explain this, but I will.  The Fibonacci series was first worked out in a text book on the "new" Arabic numerals, and turned up in a worked calculation on breeding rabbits.  Look it up if you need more.

The series goes 1, 1, 2, 3, 5, 8, 13, 21, 34 ... where each term is the sum of the two terms before it.  It has interesting mathematical features, but is is also interesting because it turns up quite a lot in nature. In this entry, I will deal with plants, just briefly.

When you look at the leaves coming out of a stem, they often form a spiral pattern. Choose a leaf near the bottom, and give it the number 0. Then number the leaves up the stem in order until you come to one that is directly above leaf zero. This will usually be leaf 5 or leaf 8.

Then if you count the number of times an ant would go around the stem, walking from the first to the last leaf, the number will usually be the previous Fibonacci term (3 or 5). The ratio 3/5 or 5/8 is called the phyllotaxis of the plant.

What you do with this is up to you. There must be a good practical reason for the way the Fibonacci numbers bob up, but what is it? And do different species in the same genus (or in the same family) have the same phyllotaxis?

Incidentally, if you look at the number of petals on a flower, the number is very often a term in the Fibonacci series. I have an idea about why this might be, but I will only say that Goethe would probably have agreed (that's a weird hint which is probably no use at all!). You work it out!

This theme continues in Phi and spirals.