Archimedean spiral

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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}}}.

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