If you fly from Tucson to Denver, you can pretty much set a straight course based on any map you have, and get there in about an hour and half on Frontier Airlines. Now, if you want to fly to Beijing China, this is no longer the case, since flying "straight" does not correspond to a straight line on most maps large enough to have both Tucson and Beijing on them. The shortest flight actually follows a great circle on the globe, and would take you near the polar region instead of straight over the Pacific. How do we find these short paths? How do you know there isn't a shorter path? We will attack these problems in a slightly different context: if the Earth were the surface of a cube or other polyhedron. We will build polyhedral models and use paper, rulers, protractors, and whatever else we can think of to try to find and understand shortest paths along the surface.