Swastika curve

The swastika curve.

The swastika curve is the name given by Martyn Cundy and A. P. Rollett in their book Mathematical Models to a type of quartic plane curve.

Equations

The plane curve with the Cartesian equation

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

or, equivalently, the polar equation

$r^{2}={\frac {\sin(\theta )\cos(\theta )}{\sin ^{4}(\theta )-\cos ^{4}(\theta )}}=-{\frac {\tan(2\theta )}{2}}.\,$

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

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

External links

• "Swastika Curve". Mathworld.