Swastika curve

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The swastika curve.
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^2 - y^2 = 2xy(x^2 + y^2). \,

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