The world is filled with spherical imagery: patterns on soccer balls, panoramic photos, and even the globe itself. How can the curved surface of a sphere be flattened to fit on the planes (paper, computer screens) we use every day? What distortions do cartographers introduce when they flatten the globe, and is there a better way to represent the earth on which we live? Mathematician David Swart expertly transitions between these two types of geometry, bringing us all along as we both flatten spheres and reconstitute the round from the flat.