Kampyle of Eudoxus

$\begin{figure}\begin{center}\BoxedEPSF{eudoxuss_kampyle.epsf}\end{center}\end{figure}$

A curve studied by Eudoxus in relation to the classical problem of Cube Duplication. It is given by the polar equation

$\begin{displaymath} r\cos^2\theta=a, \end{displaymath}$

and the parametric equations

$\begin{eqnarray*} x&=&a\sec t\\ y&=&a\tan t\sec t \end{eqnarray*}$

with $t\in [-\pi/2,\pi/2]$ .

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 141-143, 1972.

MacTutor History of Mathematics Archive. ``Kampyle of Eudoxus.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Kampyle.html.