**Logarithmic spirals**

The French mathematician and philosopher René Descartes (1596-1650) was the first to describe the spiral, which is now called a logarithmic spiral. However, it was the Swiss mathematician Jacob Bernoulli (1654-1705), fascinated by its extraordinary mathematical properties, who called it *spira mirabilis*, "marvelous spiral" in Latin.

As the size of this spiral increases, its shape remains the same, as it expands at a constant rate in a geometric progression. These beautiful spirals, also called equiangles or exponential spirals, are found everywhere in nature, in living creatures, in galactic hurricanes and other natural phenomena.

The **nautilus shell** has some of the most beautiful, graceful and recognizable spirals in nature.

The nautilus, while passing from one compartment to another, larger, fills the previous one of gas and closes it completely of a mother-of-pearl plug. It occupies only the last of the lodges, but leaves behind it a tiny thread which winds up to the lodge of origin. Each additional compartment is proportional to the previous one, a geometrical figure whose angle formed with the center of origin is maintained with the wire of growth.

The shell and the Mandelbrot spiral are in fact derived from the Fibonacci spiral, also called the **golden spiral**.