Abstract: Just a few thousand years ago, all scientific philosophers believed the Earth to be flat.  A variety of observations eventually led us to believe otherwise, and this was eventually indisputably confirmed by Magellan's circumnavigation voyage.  This discovery had incredibly significant consequences on our understanding of the world, as well as our ability to map it.  In this talk we begin by explaining how the Earth was determined to be round, describe the difficulties involved in accurately mapping it, and conclude by considering possible shapes of the universe.