\begin{definition}[Definition:Curvature/Cartesian Form]
Let $C$ be a curve defined by a real function which is twice differentiable.
Let $C$ be embedded in a cartesian plane.
The '''curvature''' $\kappa$ of $C$ at a point $P = \tuple {x, y}$ is given by:
:$\kappa = \dfrac {y''} {\paren {1 + y'^2}^{3/2} }$
where:
:$y' = \dfrac {\d y} {\d x}$ is the derivative of $y$ {{WRT|Differentiation}} $x$ at $P$
:$y'' = \dfrac {\d^2 y} {\d x^2}$ is the second derivative of $y$ {{WRT|Differentiation}} $x$ at $P$.
\end{definition}