The Complement of the Hugelschaffer’s Construction of the Egg Curve

Abstract

Hügelschäffer’s construction, based on the distortion of the ellipse construction, provides an egg-shaped curve. This curve is a mixed cubic curve, the cubic hyperbolic parabola of type A. Curve is a three-branched and except the oval arising from mentioned construction, it contains two more branches which converge towards two asymptotes: one linear and one parabolic asymptote. Since the Hügelschäffer’s construction does not give a solution for this part of the curve, we discussed the possibility of amendments to this construction, so that the entire course of the curve could be graphically processed. We came to a solution using Cartesian hyperbole complementary to the circles from Hügelschäffer’s construction.