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.

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

• Mathematics portal

• Cotes's spiral  – Plane curve

References

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