Nothing happens in the universe without some rule of maximum or minimum appearing.

— Leonhard Euler, 1744

For Leibniz and Euler, nature is made in the best possible way, and therefore follows rules. In our language: the reasoning (méthode) of the creator is in the traits (graphiko’s) of nature (physis), and it is up to us to decipher them (máthema). The same drawings appear in the most different places:

Armadillo carapace: hexagonal plates.
Armadillo carapace: hexagonal plates.Euler’s Eyes Collection
Earth's crust: basalt columns in hexagons, formed when lava cools.
Earth’s crust: basalt columns in hexagons, formed when lava cools.Euler’s Eyes Collection
Tenon: again, the hexagonal pattern.
Tenon: again, the hexagonal pattern.Euler’s Eyes Collection
Nautilus shell: a logarithmic spiral.
Nautilus shell: a logarithmic spiral.Euler’s Eyes Collection
Egg: The oval curve distributes pressure like an arc.
Egg: The oval curve distributes pressure like an arc.Euler’s Eyes Collection
Starfish: pentagonal symmetry.
Starfish: pentagonal symmetry.Euler’s Eyes Collection

The nautilus spiral has a direct connection with Descartes: he was the one who first described it, in a letter from 1638 to Mersenne. It always grows at the same rate, which is why the shell changes size without changing shape:

Descartes’ equiangular spiral. Change the growth per turn: the angle with the spokes remains the same throughout the turn.

All topics by René Descartes · ← The word “function” · Infinity and division by zero →

Credits and sources of images.