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

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

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

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References

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

External links

"Swastika Curve". Mathworld.

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