This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The emergence of non-Euclidean geometries in the 19th century rocked the foundations of mathematical knowledge and certainty. The tremors can still be felt in undergraduate mathematics today where encounters with non-Euclidean geometry are novel and often shocking to students. Because of its divergence from ordinary and comfortable notions of…