Do the Angles of a Triangle Add up to 180°? - Introducing Non-Euclidean Geometry

Abstract

How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways of introducing non-Euclidean geometry to students and the general public using different physical models, including chalksphere, crocheted hyperbolic surfaces, curved folding, and polygon tilings. Spherical geometry offers a simple yet surprising introduction to the topic, whereas hyperbolic geometry is an entirely new and exciting concept to most. Non-Euclidean geometry demonstrates how crafts and art can be used to make complex mathematical concepts more accessible, and how mathematics itself can be beautiful, not just useful.