Tuesday, September 09, 2008

Sunflower mathematics

During a break at Jubilee, I chanced upon this sunflower. To start with, this is not one single flower but a head (composite flower) of numerous florets (small flowers). The florets mature into black and white striped sunflower seeds. The sunflower seed, of course, is actually the fruit of the plant. The seed is inside the inedible husk.

In Lanzhou, we found people carrying what looked like deep-dish pizzas, which turned out to be sunflowers sold as snacks at two to four reminbi a head. You don’t eat the flower, of course; you eat the seeds. I bought one of the bigger ones, and it is now drying in my office.

Take a close look at the florets. Each is oriented at an angle to its neighbours - that angle is called the golden angle. Because of this, the florets form a pattern of successive left and right spirals - and the number of left spirals and the number of right spirals are successive Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...) - where each number is the sum of the previous 2 numbers, except for the first 2. This one has 34 in one direction and 55 in another on the outside - count them. I was told bigger ones have 89 and 144 but I haven’t verified it yet.

Amazing, isn’t it? Why did God make them this way, I wonder?

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