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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.




© 1996-9 Eric W. Weisstein
1999-05-26