Definition:Curvature/Cartesian Form

Definition
Let $C$ be a curve defined by a real function which is twice differentiable. Let $C$ be embedded in a cartesian plane.

The curvature $k$ of $C$ at a point $P = \left({x, y}\right)$ is given by:


 * $k = \dfrac {y''} {\left({1 + y'^2}\right)^{3/2} }$

where:
 * $y' = \dfrac {\mathrm d y} {\mathrm d x}$ is the derivative of $y$ $x$ at $P$
 * $y'' = \dfrac {\mathrm d^2 y} {\mathrm d x^2}$ is the second derivative of $y$ $x$ at $P$.

Also see

 * Equivalence of Definitions of Curvature