Mathematics of Floating 3D Printed Objects

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 additionally explore

the influence of changing an object's center of gravity. For objects with square

cross section, for example, this breaks the symmetry observed in the uniform density case.

We design and create 3D printed objects, float them, and compare the observations

to the theoretical predictions.