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.