  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.
