# 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

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

or, equivalently, the polar equation

${\displaystyle r^{2}=-\tan(2\theta )/2.\,}$

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

${\displaystyle x^{4}-y^{4}=xy.\,}$
1. ^ Mathematical Models by H. Martyn Cundy and A.P. Rollett, second edition, 1961 (Oxford University Press), p. 71.