**Cartesian equation: ** 3*a* *y*^{2} = *x*(*x*-*a*)^{2}

**Click below to see one of the Associated curves.**

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

This curve was investigated by Tschirnhaus, de L'Hôpital and Catalan. As well as Tschirnhaus's cubic it is sometimes called de L'Hôpital's cubic or the trisectrix of Catalan.

The name Tschirnhaus's cubic is given in R C Archibald's paper written in 1900 where he attempted to classify curves.

Tschirnhaus's cubic is the negative pedal of a parabola with respect to the focus of the parabola.

The caustic of Tschirnhaus's cubic where the radiant point is the pole is Neile's semi-cubic parabola .

JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Tschirnhaus.html