Here we give a discovery activity that we have used, in its entirety, with undergraduate students studying non-Euclidean geometry. We use freeware Geometry Playground [1] for these investigations; simply select the main link on the Geometry Playground page to run it. Geometry Playground allows straightedge and compass construction in Euclidean and non-Euclidean geometries such as spherical and hyperbolic. We let \(r\) represent the radius of a circle as measured in each geometry, while \(C\) and \(A\) represent the circumference and area of that circle, again as measured within that geometry.