Tschirnhausen Cubic

$\begin{figure}\begin{center}\BoxedEPSF{tschirnhausen_cubic.epsf scaled 600}\end{center}\end{figure}$

The Tschirnhausen cubic is a plane curve given by

$\begin{displaymath} a=r\cos^3\left({{\textstyle{1\over 3}}\theta}\right), \end{displaymath}$

and is also known as Catalan's Trisectrix and L'Hospital's Cubic. The name Tschirnhaus's cubic is given in R. C. Archibald's 1900 paper attempting to classify curves (MacTutor Archive). Tschirnhaus's cubic is the Negative Pedal Curve of a Parabola with respect to the Focus.

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 87-90, 1972.