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.

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