Poinsot's spirals

The Poinsot spiral r=csch(θ/3).

The Poinsot spiral r=sech(θ/3).

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.

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