The curvature of a function of two variables, `f`(`x`_{1}, `x`_{2}) is the product of all partial second derivatives with respect to like variables (e.g. ∂^{2}`f`/∂`x`_{1}^{2}), minus the product of all second partial derivatives with respect to different variables (e.g. ∂^{2}`f`/∂`x`_{1}∂`x`_{2}).

For two variables, this is (∂^{2}`f`/∂`x`_{1}^{2})(∂^{2}`f`/∂`x`_{2}^{2}) - (∂^{2}`f`/∂`x`_{1}∂`x`_{2})^{2} (because ∂^{2}`f`/∂`x`_{1}∂`x`_{2} = ∂^{2}`f`/∂`x`_{2}∂`x`_{1}).

In Eindhoven notation, this is (* : 0 ≤ `i` ≤ `n` : ∂^{2}`f`/∂`x`_{i}^{2}) - (* : 0 ≤ `i` ≤ `n` ∧ 0 ≤ `j` ≤ `n` ∧ `i` ≠ `j` : ∂^{2}`f`/∂`x`_{i}∂`x`_{j}).

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.