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 space, non-Euclidean geometry can be a setting in which to provide students with authentic mathematical experiences. This article presents a model of the hyperbolic plane--the Missing Disk model--that is not developed in textbooks, and attempts to exemplify the chain of reasoning that a group of undergraduate students might undertake to develop it. This article discusses ways in which it may be used in a non-Euclidean geometry class to engage students in authentic mathematical activities. (Contains 8 figures and 4 footnotes.)