Publication Year



Mathematics, geometry, Lorentzian, number plane, hyperbolic


Applied Mathematics | Geometry and Topology | Mathematics | Physical Sciences and Mathematics


The hyperbolic number plane (also known as perplex numbers) was invented by four freshmen from St. Olaf College in 1981. Supported by a grant from the National Science Foundation, these students (P. Borman, E. Heppner, B. Nelson, and K. Olstad) were given an opportunity to experiment with mathematics. Their work was entirely based on the assumption that there exists some number whose absolute value is -1, an idea which one student had curiously proposed while in high school. In the process of development, the young mathematicians discovered a link between hyperbolic numbers and physics. In particular, it was found that hyperbolic numbers provided a coordinate system for Lorentzian geometry, a mathematical model used to understand Einstein's theory of special relativity. Hence, the objective of this paper is to explore the hyperbolic number plane and show that it has a practical application.

Department 1 Awarding Honors Status