Inversive Geometry III: Inverting an Ellipse

Under inversion, a circle transforms into a circle (or a line if it goes through the center of inversion). This Demonstration shows that ellipses in general are inverted into more complicated shapes. These shapes arise from the mapping in the case of inversion on the unit circle, which transforms the ellipse into the quartic . In this Demonstration the pink disk is the circle of inversion. To detail this mapping the ellipse is divided into a variable number of rings that are also inverted. To enhance the effect when the three handles (red circles) are varied, optional shading is also provided.