Poinsot's spirals

Two spirals represented by polar equations

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

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

  • iconMathematics 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.
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