Definition:Curvature/Polar Form

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Let $C$ be a curve defined by a real function which is twice differentiable.

Let $C$ be embedded in a polar plane.

The curvature $\kappa$ of $C$ at a point:

$P = \polar {r, \theta}$

is given by:

$\kappa = \dfrac {\paren {\map \arctan {\dfrac {r \theta'} {r'} } }' + \theta'} {\paren {r'^2 + \paren {r \theta'}^2}^{1/2} }$

Also see

  • Results about curvature can be found here.