On the Maximum Circular Inverses of Maximum Circles

Abstract

In this study, the inverses of maximum circles under the maximum circular inversion are examined. The maximum circular inversion is observed to transform maximum circles to curves consisting of parabolic arcs, line segments, and sometimes rays. It is seen that the image curve occurs in different shapes depending on the relative positions of the inversion circle and the maximum circle. While the images of maximum circles not passing through the inversion center are closed curves, the images of those passing through the inversion center are not closed. Inverse curves have been studied by considering the radii of the maximum circles and the positions of the lines joining their centers and the center of maximum inversion. Classifications of the inverses of maximum circles are presented.