  We explore the stability of floating objects through mathematical modeling
and experimentation. Our models are based on standard ideas of center of
gravity, center of buoyancy, and Archimedes' Principle. We investigate a
variety of floating shapes with two-dimensional cross sections and identify
analytically and/or computationally a potential energy landscape that helps
identify stable and unstable floating orientations. We compare our analyses and
computations to experiments on floating objects designed and created through 3D
printing. In addition to our results, we provide code for testing the floating
configurations for new shapes, as well as giving details of the methods for 3D
printing the objects. The paper includes conjectures and open problems for
further study.
