Natural Parametric Equations

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length , instead of an arbitrary variable like .

For example, while the usual parametric equations for circle of radius centered at the origin are given by

			(1)
			(2)

since the arc length function is given by

(3)

the natural parametric equations are

			(4)
			(5)