Fix a small circle to the rim of a larger one and turn both, following a point on the smallest. Ancient astronomers used these epicycles to predict the wandering of the planets in the night sky. Centuries later, Joseph Fourier showed why they work so well: almost any repeating shape can be built by adding together circular motions of different sizes and speeds.

Lemniscate Infinity. Jacob Bernoulli’s figure-eight from 1694, the curve behind the infinity sign.