Capstone Studies on Roots of Hyperbolic Numbers

To help students develop a more creative and inquisitive mathematical mindset, we present capstone-style explorations on finding roots of hyperbolic numbers, a generalization of the complex numbers. We include pedagogical reflections, informed by our use of the activities in a capstone course. The explorations are suitable (and challenging!) for undergraduates who are embarking on more abstract mathematics beyond the standard calculus sequence. Students will engage in mathematically enriching tasks such as looking for geometric meaning in algebra, drawing conclusions from equations without solving them, working in hyperbolic coordinates, and making and testing their own conjectures. The explorations may be used in a variety of research-style learning environments, such as a capstone course, an honors project, or an undergraduate research experience.