Fermat’s spiral

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

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

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

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