In this paper we investigate inversion about the unit circle from a complex perspective. Using complex rational functions we develop methods to construct curves which are self-inverse (anallagmatic). These methods are then translated to the split-complex numbers to investigate the theory of inversion about the unit hyperbola. The analog of the complex analytic techniques allow for the construction and study of anallagmatic curves about the unit hyperbola.

Author Bio

Stephanie Neas completed this work during the summer of 2016, funded by the University of Wisconsin-Stout Foundation. She also has an interest in writing and reading, and is planning to attend graduate school after finishing her undergraduate degree.