Poinsot s spirals

Short description: Two spirals represented by polar equations

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

r=a csch⁡(nθ)
r=a sech⁡(nθ)

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

* Cotes's spiral

## References

1. ↑ Lawrence, J. Dennis (1972). A Catalog of Special Plane Curves. New York: Dover. pp. 192–194. ISBN 0486602885. https://archive.org/details/catalogofspecial00lawr/page/192.

* v
* t
* e

Spirals, curves and helices

Curves|

* Algebraic
* Curvature
* Gallery
* List
* Topics

Helices|

* Angle
* Antenna
* Boerdijk–Coxeter
* Hemi
* Symmetry
* Triple

| Biochemistry|

* 310
* Alpha
* Beta
* Double
* Pi
* Polyproline
* Super
* Triple
* Collagen

|

Spirals|

* Archimedean
* Cotes's
* Epispiral
* Hyperbolic
* Poinsot's
* Euler
* Fermat's
* Golden
* Involute
* List
* Logarithmic
* On Spirals
* Theodorus

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Poinsot's spirals. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Poinsot's_spirals&oldid=234309"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template