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, but 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.

External links

• Mathworld Article