# Definition:Curvature/Polar Form

## Definition

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:

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