You Have to Draw the Line: Constructions in Hyperbolic Geometry
Summary: Exploring hyperbolic geometry in a GeT course can enrich the student experience by offering a contrast to the more familiar Euclidean world. In a geometry where lines have very different properties than in Euclidean geometry, students are forced to reconsider what they consider to be “true” or “obvious”. On the other hand, conceiving of a universe where parallel lines are not everywhere equidistant can be a challenge! The models of non-Euclidean geometry provide an elegant solution to this difficulty. They offer students opportunities to explore hyperbolic geometry in a hands-on manner and to visualize its theorems.
In this seminar, we’ll explore constructions in the Poincaré and Klein models of hyperbolic geometry. We’ll use dynamic geometry software to create hyperbolic “line-maker” and “circle-maker” construction tools and we’ll use those tools to develop hyperbolic analogs to standard Euclidean constructions. We will also see how these constructions can be used both to enhance student understanding of hyperbolic geometry and to strengthen student facility with regular Euclidean constructions.
Duration: 60 minutes
Format: Online seminar via Zoom web meeting software with questions and discussion. Detailed instructions for joining the seminar will be emailed to registered participants.
Stephen Szydlik is a professor of mathematics at the University of Wisconsin Oshkosh. He earned his M.A. and PhD. in mathematics from the University of Wisconsin, where he studied hyperplane arrangements under Dr. Peter Orlik. Over the course of his career, he has published research in both mathematics and mathematics education, and he especially enjoys finding connections between diverse areas of mathematics. His most recent scholarship linked social choice theory with the scoring of cross-country running races. He taught a GeT course during his first year at UWO, and it quickly became his favorite course. His seminar talk arises out of his experiences teaching that course.