# Poinsot's spirals

In mathematics, Poinsot's spirals are two spirals represented by the polar equations

$r = a\ \operatorname{csch} (n\theta)$
$r = a\ \operatorname{sech} (n\theta)$

where csch is the hyperbolic cosecant, and sech is the hyperbolic secant.[1] They are named after the French mathematician Louis Poinsot.

The Poinsot spiral r=csch(θ/3).
The Poinsot spiral r=sech(θ/3).
Examples of the two types of Poinsot's spirals.