Plateau Curves

$\begin{figure}\begin{center}\BoxedEPSF{PlateausCurve.epsf scaled 700}\end{center}\end{figure}$

A curve studied by the Belgian physicist and mathematician Joseph Plateau. It has Cartesian equation

$\displaystyle x$	$\textstyle =$	$\displaystyle {a\sin[(m+n)t]\over\sin[(m-n)t]}$
$\displaystyle y$	$\textstyle =$	$\displaystyle {2a\sin(mt)\sin(nt)\over\sin[(m-n)t]}.$

, the Plateau curve degenerates to a Circle with center

and radius 2.

References