Signed curvature of a plane graph
= Signed curvature of a plane graph
{title2=$\kappa=\dfrac{u_{xx}}{(1+u_x^2)^{3/2}}$}
For an oriented plane curve written locally as the graph $(x,u(x))$, its signed curvature is
$$
\kappa=\frac{u_{xx}}{(1+u_x^2)^{3/2}}.
$$
The equation $\kappa=0$ describes straight lines, while $\kappa=1/R$ describes consistently oriented arcs of circles of radius $R$.