Do the Angles of a Triangle Add up to 180{\deg}? -- Introducing Non-Euclidean Geometry

TL;DR

This paper explores engaging methods to introduce non-Euclidean geometry to students and the public through physical models and art, highlighting its beauty and accessibility beyond traditional rules.

Contribution

It presents diverse physical models and artistic approaches to make non-Euclidean geometry accessible and captivating for learners and the general public.

Findings

Physical models enhance understanding of non-Euclidean geometry.

Artistic representations make complex concepts more accessible.

Non-Euclidean geometry can be taught as a creative and beautiful subject.

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.