Quadratrix of Hippias

The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Archive). It can be used for angle trisection or, more generally, division of an angle into any integral number of equal parts, and circle squaring.

It has polar equation

(1)

with corresponding parametric equation

			(2)
			(3)

and Cartesian equation

(4)

Using the parametric representation, the curvature and tangential angle are given by

			(5)
			(6)

for .