The curve was studied by von Tschirnhaus, de L'Hôpital, and Catalan. It was given the name Tschirnhausen cubic in a 1900 paper by R C Archibald, though it is sometimes known as de L'Hôpital's cubic or the trisectrix of Catalan.
Put . Then applying triple-angle formulas gives
If the curve is translated horizontally by 8a then the equations become
This gives an alternate polar form of
- J. D. Lawrence, A Catalog of Special Plane Curves. New York: Dover, 1972, pp. 87-90.
- Weisstein, Eric W., "Tschirnhausen Cubic", MathWorld.
- "Tschirnhaus' Cubic" at MacTutor History of Mathematics Archive
- "Cubique de Tschirnhausen" at Encyclopédie des Formes Mathématiques Remarquables (in French)
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