# Poinsot's spirals

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

Mathematics includes the study of such topics as quantity, structure, space, and change.

In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.

## Contents

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

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

Louis Poinsot was a French mathematician and physicist. Poinsot was the inventor of geometrical mechanics, showing how a system of forces acting on a rigid body could be resolved into a single force and a couple.

## 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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## References

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