Swastika curve

The swastika curve is the name given by Cundy and Rollett[1] to a type of quartic plane curve.

The swastika curve.

Equations

The quartic plane curve with the Cartesian equation

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

or, equivalently, the polar equation

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

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

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

References

1. H. Martyn Cundy; A.P. Rollett (1961). Mathematical Models (second ed.). Oxford University Press. p. 71.

External links

• "Swastika Curve". Mathworld.