Poinsot's spirals

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

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

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

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