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# 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

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

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