Article Title

Making Waves


As explored in [1], the structure of the hyperbolic numbers encodes characteristics of two-dimensional Minkowski spacetime. Di erentiable functions on the hyperbolic numbers provide solutions to the wave equation. In this paper we analogize the method of conformal mappings to the hyperbolic numbers in order to provide solutions to the wave equation on given regions with given boundary constraints. As template solutions we use low-degree polynomials and the logarithm function, and as transformations we use polynomials and simple rational functions. We conjecture (and nearly show) that in general, the family of rational functions we use take hyperbolas to hyperbolas.