This is a translation of:
Hidden Mathematics in Nature.
By José de Toledo. The imaginary line spiral that
crosses a Shell
There are In the nature some curious coincidences. Did you know, by instance, that the
number of seeds of a spiral of a sunflower and the petals of many flowers
follow the same pattern that the shell of a snail or a Nautilus. This relation, though it does not looks to be true,
is not causal, but it answers to a serie of mathematical formulae that
appear repetidely in a great number of alive beings. They are the
patterns. The most habitual are two: the
golden number (or golden proportion) and the series of Fibonacci, which in
addition are very related between them. In both cases, their development can be
complicated to deal, but we can discover them in a natural way. In order that
you understand it, nobody calculates if the distance between the nose and the
chin is proportional to the total length of the face, but if it is like that,
we consider this person beautiful.
number is equal to 1,618... The golden spirals move away from
the center with this proportion every quarter of return; thus, also they
arrange the leaves in the branches, or the branches in the trunks. It is not a
question of a coincidence, but it is the most effective way of organizing the
structures. This pattern allows, among
other things, that the branches should grow without some do shade to others.
The leaves of
The packaging in spiral of golden proportions appears in turn in the leaves of the
artichokes or in the structures of a pineapple. In them also we find the
series of Fibonacci: the number of leaves of a spiral of artichoke always
belongs to this system; that of the opposite spiral, it is the previous or top
number of the series. A typical game between biologists is to count the above
mentioned structures in a spiral and to try to guess that of the opposite one.
Fibonacci created his famous series on having tried to discover how the baby of rabbits
to improve. The sequence relates the number of births that take place every
period of baby, beginning with the numbers zero and one, named generators. From
there the following numbers they are the sum of both previous ones: 0, 1, 1, 2,
3, 5, 8...
The model did not work very well, but much later discovered that it was serving perfectly to calculate
the number of ancestors of a macho bee: The drone is born of an egg without
fertilizing; it has, therefore a mother and no father. His mother, on the other
hand, had two parents, in such a way
that the original one has two grandparents and three great-grandfathers, two of
his grandmother and one of his grandfather, and so on, completing the series of
answers to the Fractal Geometry
Another theory, that of the fractal geometry, gives a
return of nut to the discipline, overcoming the inflexibility of the classic or
Euclidean school. The work that supposed the take off of this theory titles " The Fractal Geometry of the Nature
". From his publication in 1982, fractal patterns have not stopped
being in the nature, from the valleys of rivers up to the anatomy of the plants.
One of his characteristics reflects the invariability
of his scale; it is to say they are equal if we look at them closely or of
distant view. The classic example is that of the fern, where mathematical
function that describes the complete individual is the same that describes his
leaves or smaller parts. This allows, for example, that thanks to an IT very
simple program we could see dense forests of ferns in the cinema. This has other
applications, like to help to generate maps when the same technology is applied
to the landscapes.
Well, Nature never stops of amazing us.