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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

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

If $m = 2n$, the Plateau curve degenerates to a Circle with center $(1,0)$ and radius 2.


MacTutor History of Mathematics Archive. ``Plateau Curves.''

© 1996-9 Eric W. Weisstein