Poinsot's spirals

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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.

The Poinsot spiral r=csch(θ/3).
The Poinsot spiral r=csch(θ/3).
The Poinsot spiral r=sech(θ/3).
The Poinsot spiral r=sech(θ/3).
Examples of the two types of Poinsot's spirals.

See also[edit]

References[edit]

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