Sunflower and mathematics reveal the secret of the golden ratio

Mathematician Ben Spark of the University of Bath discovered and illustrated a new area of ​​use for the principle of harmonic proportion known as the golden ratio. It is relatively easy to implement it in hand-made objects, knowing the exact coefficients, but it turned out that there are a lot of things in nature that evolved according to this principle.

As an example, Spark cited the arrangement of seeds in a sunflower flower - in order to survive, a photophilous plant must learn to place the maximum number of seeds in a limited space. This does not depend on the size of a particular specimen, the whole point is in the principle of seed germination in a flower, which is laid down at the genetic level. A sunflower always has a center, from which the seeds diverge to the periphery with some interval, forming patterns.

In the models that Spark used, the sunflower fill patterns are built from the center with an equal pitch offset. The task: to calculate its optimal value so that in the end there are no voids and overlaps in the flower. But modeling showed that the problem cannot be solved using whole numbers and simple fractions, while the principle of the golden ratio fits almost perfectly.

That is why the sunflower looks so beautiful, orderly and neat, because it is from the point of view of mathematics. The principle that we have learned to be aware of and measure with the help of our minds, evolution took into service on its own long ago. This means that the golden ratio can be found in other natural structures.