A Disappearing Number

The swastika curve.

The swastika curve is the name given by Cundy and Rollett to the quartic plane curve with the Cartesian equation

$y^{4}-x^{4}=xy,\,$

or, equivalently, the polar equation

$r^{2}=-\tan(2\theta )/2.\,$

The curve looks similar to the right-handed swastika, but can be inverted with respect to a unit circle to resemble a left-handed swastika. The Cartesian equation then becomes

$x^{4}-y^{4}=xy.\,$

External links

• Mathworld Article