The functions $\mathrm{sn}(u\mid m)$, $\mathrm{cn}(u\mid m)$, $\mathrm{dn}(u\mid m)$ introduced by Jacobi to invert the elliptic integral of the first kind. They parametrise the nonlinear pendulum, Euler’s elastica, the rigid-body Euler-Poinsot motion, and KdV cnoidal waves.