| Abstrakt: |
This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where i 2 = − 1 , replace i by τ, where τ 2 = 1 , but where τ ≠ ± 1. This creates a new algebra and geometry that is counter-intuitive, but has parallels to familiar mathematics so that students can use what they know, but on different ground. The materials are intended to foster investigation, collaboration, and creative mathematical thinking. [ABSTRACT FROM AUTHOR] |
