Swastika curve

The swastika curve.

The swastika curve is the name given by Cundy and Rollett[1] 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. 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. \,
  1. ↑ Mathematical Models by H. Martyn Cundy and A.P. Rollett, second edition, 1961 (Oxford University Press), p. 71.

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