Swastika Curve

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

The plane curve with Cartesian equation

$\begin{displaymath} y^4-x^4=xy \end{displaymath}$

and polar equation

$\begin{displaymath} r^2={\sin\theta\cos\theta\over \sin^4\theta-\cos^4\theta}. \end{displaymath}$

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.