South Pointing Chariot: An Invitation to Differential Geometry

Abstract

We introduce the south-pointing chariot, an intriguing mechanical device from ancient China. We use its ability to keep track of a global direction as it travels on an arbitrary path as a tool to explore the geometry of curved surfaces. This takes us as far as a famous result of Gauss on the impossibility of a faithful map of the globe, which started off the field of differential geometry. The reader should get a view into how geometers think and an introduction to important early results in the field, but should need no more than a solid background in calculus (ideally through multivariable calculus). This is achieved by relying on the reader's visual intuition.