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.
"Anallagmatic Curves and Inversion About the Unit Hyperbola,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/6