Horse 614 - Not Even Solomon

I want you to go outside and find something really really boring for me. Keep on walking around the place until you find a sunflower. Now I don't know if you've actually bothered to look at one in close detail but take a closer look today.

Sunflowers are mathematical marvels. Firstly you'll find a series of spirals that head outwards from the centre. Not only this but in both directions, both clockwise and anti-clockwise, but also in the same direction at upwards of 5 angles of incidence. Only the Allianz Arena in Munich comes close to this sort of complexity.

Next I want you to do some counting. Why is it that the number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34 or 55? For example, the lily has three petals, buttercups have five of them, the chicory has 21 of them, the daisy has often 34 or 55 petals, etc.

Furthermore, when one observes the heads of sunflowers and one notices the series of curves, one winding in one sense and one in another; the number of spirals not being the same in each sense. Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? The same for pinecones - why do they have either 8 spirals from one side and 13 from the other, or either 5 spirals from one side and 8 from the other? Finally, why is the number of diagonals of a pineapple also 8 in one direction and 13 in the other?

Are these numbers the product of chance? No! They all belong to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (where each number is obtained from the sum of the two preceding). A more abstract way of putting it is that the Fibonacci numbers fn are given by the formula f1 = 1, f2 = 2, f3 = 3, f4 = 5 and generally f n+2 = fn+1 + fn . For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that one understands why. It is a question of efficiency during the growth process of plants.

Plants are incredibly compact machines. The fibonacci series of numbers roughly follow the Golden Ratio, but more importantly they're irrational. This means that there will never be any straight lines when it comes to growing seed heads. Straight lines lead to increased shade and if you happen to be a small device that loves the sun, you'd want as much of stuff as possible.

Sneaky little things... not even Solomon was wise enough to work out that.