Curves

Tschirnhaus's Cubic

Description

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 .

Associated Curves

Definitions of the Associated curves

Evolute

Involute 1

Involute 2

Inverse curve wrt origin

Inverse wrt another circle

Pedal curve wrt origin

Pedal wrt another point

Negative pedal curve wrt origin

Negative pedal wrt another point

Caustic wrt horizontal rays

Caustic curve wrt another point