The curvature of a function of two variables, f(x1, x2) is the product of all partial second derivatives with respect to like variables (e.g. ∂2f/∂x12), minus the product of all second partial derivatives with respect to different variables (e.g. ∂2f/∂x1x2).

For two variables, this is (∂2f/∂x12)(∂2f/∂x22) - (∂2f/∂x1x2)2 (because ∂2f/∂x1x2 = ∂2f/∂x2x1).

In Eindhoven notation, this is (* : 0 ≤ in : ∂2f/∂xi2) - (* : 0 ≤ in ∧ 0 ≤ jnij : ∂2f/∂xixj).

A zero curvature corresponds to a flat surface, positive curvature means it looks a bit like the surface of a sphere, and negative curvature looks like a saddle.