Editing Plane curve (section)

==Smooth plane curve==
A smooth plane curve is a curve in a [[real number|real]] Euclidean plane {{tmath|\R^2}} and is a one-dimensional [[smooth manifold]]. This means that a smooth plane curve is a plane curve which "locally looks like a [[line (geometry)|line]]", in the sense that near every point, it may be mapped to a line by a [[smooth function]].
Equivalently, a smooth plane curve can be given locally by an equation <math>f(x, y) = 0,</math> where {{tmath|f: \R^2 \to \R}} is a [[smooth function]], and the [[partial derivative]]s {{tmath|\partial f/\partial x}} and {{tmath|\partial f/\partial y}} are never both 0 at a point of the curve.