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. They are named after the French mathematician Louis Poinsot.

Examples of the two types of Poinsot's spirals

The Poinsot spiral r=csch(θ/3).

The Poinsot spiral r=sech(θ/3).

See also

• Cotes's spiral