Fermat’s spiral

The parametric equations of the Fermat’s spiral can be given by 

$x = at^{\frac{1}{2}} \cos t, \, y= at^{\frac{1}{2}} \sin t $

$x = -at^{\frac{1}{2}} \cos t, \, y= -at^{\frac{1}{2}} \sin t$ 

In polar coordinates the equation of a Fermat’s spiral with parameter a and centre $(0, 0)$ is given by

$r^2=a^2 \theta.$

Source: en1gm4th5