Introduction: Hyperbolic Geometry and Its Models Hyperbolic geometry resides in a unique but challenging position within the GeT curriculum, providing powerful opportunities for an instructor to enrich student understanding of geometry. First, it provides experiences with a significant axiom system distinct from Euclidean geometry. Second, by changing a single axiom (the parallel postulate), it provides a […]

“One must be able to say at all times – instead of points, straight lines, and planes – tables, chairs, and beer mugs. “David Hilbert [4] Axioms serve as fundamental bricks in the foundations of mathematics. Given a small collection of statements assumed to be true, a universe of subsequent truths may spring forth, grounded in […]

​​Four questions with Stephen Szydlik, Professor of Mathematics at the University of Wisconsin Oshkosh

We are all members of the Euclidean Archetype workgroup. As we summarized in our report, a GeT course organized around the Euclidean archetype will focus on the axiomatic development of fundamental principles of geometry. Informed by the spirit and organization of Euclid’s Elements, this course emphasizes mathematical precision, rigorous proof, and clear communication. We have […]