Archimedean spiral

An Archimedean spiral is a spiral with the polar equation

$$r=a{\theta }^{1/t},$$

where $a$ is a real, $r$ is the radial distance,$\theta$ is the angle, and $t$ is a constant.

The curvature of an Archimedean spiral is given by the formula

$$\frac{t{\theta }^{1-1/t}(t^2{\theta }^2+t+1)}{a{(t^2{\theta }^2+1)}^{3/2}}.$$