The shellswith their fascinating forms, seem to be designed by a skilled sculptor. Observing a shell closely, one realizes that his spiral is an incredibly precise geometry, as if he had been designed with mathematical rules. But how is it possible that nature creates something so perfect?
How a shell is made and what it is for
The shells are protective shells that are built by molluscs to protect themselves and support their soft body, which otherwise would be completely exposed to predators or impacts. Most of the composition of a shell is made of CArbonion of footballa mineral substance that constitutes about the 95% of his volume. The remainder 5% is composed of organic substances, such as proteins and other macromoleculeswhich make the shell flexible, resistant and capable of growing continuously. One of the fascinating characteristics of the shells is that they never stop growing. When the mollusk grows, even its shell must adapt to the new dimensions. This process takes place thanks to the mollusk cloak, the outermost layer, which secrete proteins that form a sort of scaffolding. Football carbonate binds to this structure, creating new layers that are added to the previous ones, maintaining regular growth.
It is precisely this regular growth rhythm that gives shape to the perfect spiral of the shell. But how is it possible that it grows in this precise way?
There spiral of fibonacci
There mathematics Get involved: one of the most common forms we see on the shells is the logarithmic spiral.
Before exploring this type of spiral, it is useful to talk about the Succession of Fibonaccia sequence that begins with 0 and 1, and where each next number is the sum of the previous two, starting from the initial numbers 0 and 1 (0+1 = 1, 1+1 = 2, 1+2 = 3 …). In this sequence the relationship between two consecutive numbers tends to infinity towards a fixed value, approximately 1.618. This number is known how Aurea sectiona value that is associated with perfect proportions in mathematics and arts. By building squares whose side corresponds to each number of the fibonacci sequence, a spiral is obtained. This is the spiral of fibonacciwhich resembles that of a shell, but that’s not quite.
The logarithmic spiral
The spirals of the shells are not all the same, but follow the same structure as a spiral of fibonacci, at least approximately. Fibonacci’s spiral is in fact a good approximation of the Aurea spirala type of spiral in which the relationship between the rays of the circumference arches that make up the spiral itself is always the same as the golden section (1.618). The golden spiral is in turn a particular type of a wider category of spirals, the logarithmic spirals.
The logarithmic spiral It has a unique property: it grows keeping a constant proportion, but not necessarily equal to the golden section. As the spiral develops, each lap enlarges in proportion to the previous lap, giving life to a spiral that, although enlarged, always maintains the same shape. And the molluscs make just like that: they slowly add new material, but they do not make it evenly, they do it in proportion to the material already present, thus giving life to a precise logarithmic spiral. One of the characteristics of this form is his self-membarity: It doesn’t matter how much you enlarge or kneel, the spiral remains the same precisely because of the proportions between its parts that remain constant for all the stairs. In practice, if we observe the shell of a mollusc when it is very small and when it has completely grown, the shell will appear identical in its general form, only on a different scale, as if it had been “zoomed”.
The shape of the logarithmic spiral is not only aesthetically fascinating, but also extremely functional. Growing in this way, the shell not only maintains its shape, but allows the mollusk of Add new material efficientlywithout having to constantly redesign the structure. This allows the mollusk to grow without too many efforts, minimizing energy consumption.
But the logarithmic spiral is not an exclusive phenomenon of shells. It can also be observed in other natural contexts, as in the flight trajectory of the Pellegrino hawkwho during his beaten follows a logarithmic spiral to maintain his prey in his visual field. In addition, the sunflower organizes its seeds by approximately following a logarithmic spiral, optimizing the space on the surface of the flower.
After all, mathematics is everywhere. The forms that are observed in nature are not random, but follow precise patterns that allow living beings to grow, move and adapt efficiently. Mathematics is the language with which nature speaksand thanks to it it is possible to read its secrets. The beauty of nature, therefore, is not only aesthetic, but it is deeply mathematical.
