The arrangement of seeds on the head of a sunflower is a very good example of the Fibonacci sequence. By closely observing the seed configuration we notice two series of curves, one winding in one direction and one in another. The numbers of spirals are not the same in each direction. If we count the number of spirals given in the figure, we notice the number is 21 and the number of spirals in the opposite direction is 34.
Coincidentally, this number is within the Fibonacci sequence. The numbers of spirals are not the same in each direction. In general they are either, 21 and 34, or 34 and 55, or 55 and 89 or 89 and 144. In principle all the sunflowers show a number of spirals that are within the Fibonacci sequence.
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 because of the efficiency during the growth process of plants.
In many cases, the head of a flower is made up of small seeds which are produced at the centre, and then migrate towards the outside to fill eventually all the space. Each new seed appears at a certain angle in relation to the preceding one. In order to optimize the filling, it is necessary to choose the most irrational number there is. This number is exactly the golden mean. The corresponding angle, the golden angle is 137.5 degrees. This angle has to be chosen very precisely. Even the variation of 1/10 of a degree destroys the optimization completely. When the angle is exactly the golden mean, two families of spirals (one in each direction) are then visible. Moreover, generally the petals of flower are formed at the extremity of one of the families of spiral. This explains why the number of petals corresponds on average to a Fibonacci number.
We learn that Nature is fortunately a much better Mathematician than most of us.
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 because of the efficiency during the growth process of plants.
In many cases, the head of a flower is made up of small seeds which are produced at the centre, and then migrate towards the outside to fill eventually all the space. Each new seed appears at a certain angle in relation to the preceding one. In order to optimize the filling, it is necessary to choose the most irrational number there is. This number is exactly the golden mean. The corresponding angle, the golden angle is 137.5 degrees. This angle has to be chosen very precisely. Even the variation of 1/10 of a degree destroys the optimization completely. When the angle is exactly the golden mean, two families of spirals (one in each direction) are then visible. Moreover, generally the petals of flower are formed at the extremity of one of the families of spiral. This explains why the number of petals corresponds on average to a Fibonacci number.
We learn that Nature is fortunately a much better Mathematician than most of us.
