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.

Examples of the two types of Poinsot's spirals

The Poinsot spiral r=csch(θ/3).

The Poinsot spiral r=sech(θ/3).

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Lawrence, J. Dennis (1972). A Catalog of Special Plane Curves. New York: Dover. pp. 192–194. ISBN 0486602885.

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