Kappa Curve

A curve also known as Gutschoven's curve which was first studied by G. van Gutschoven around 1662 (MacTutor Archive). It was also studied by Newton and, some years later, by Johann Bernoulli. It is given by the Cartesian equation

(1)

by the polar equation

(2)

and the parametric equations

			(3)
			(4)

The curvature and tangential angle are given by

			(5)
			(6)