## Cayley's Sextic

A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper published in Strasbourg in 1900 (MacTutor Archive). Cayley's sextic is given in Polar Coordinates by

 (1)

or
 (2)

where . In the latter case, the Cartesian equation is
 (3)

The parametric equations are
 (4) (5)

The Arc Length, Curvature, and Tangential Angle are

 (6) (7) (8)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 178 and 180, 1972.

MacTutor History of Mathematics Archive. Cayley's Sextic.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cayleys.html.