What is surprising is the frequent occurrence of the golden section and the Fibonacci numbers in nature. These structural principles are most conspicuous in the arrangement of leaves and in the inflorescence of some plants, for example in the sunflower, in certain kinds of cabbage, fircones, in many species of palms and in the petals of a rose.
The leaves of this plant are arranged so that two consecutive leaves divide the entire circle in the proportions of the golden section. In other words: the angle between them amounts to about 137.5 degrees – the golden angle.
The reason for this arrangement is probably that in this way a new leaf or a new seed kernel always appears where there is the most space for it. As the angle is based on an irrational number, one leaf will never end up lying exactly over the other. This allows the sunlight coming from above to be ideally used.
An especially good example of the occurrence of Fibonacci numbers in nature is the sunflower’s head of seeds. Here clearly visible Fibonacci spirals develop. The individual seeds in this case correspond to the leaves of the ((vorherigen Pflanze)) and like them are arranged according to the golden angle. The deviation from the mathematical golden angle is less than 0.01 per cent. Seeds that grow consecutively are thus arranged far apart in space. Mathematically it can be shown that such seeds are situated close to one another.
If we consider the number of arcs which turn to right it will hardly be a surprise: here, too, we have consecutive Fibonacci numbers. In the outer area of sunflowers there are usually 34 and 55 spirals, in the case of larger specimens 55 and 89 or even 89 and 144. Whether the larger number of arcs are right-hand turning or left-hand turning is, however, left to chance.
In this way the seeds are packed most densely, as can easily be shown if the angle between two seeds that have grown consecutively is changed.
Einen Kommentar hinterlassen