Archimedean spiral
ArchimedeanSpiral
2003-12-09 11:24:59
2007-06-10 12:00:22
Definition
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An \emph{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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