2015/02/24 by Stephen Sawin, Sawin, Stephen
Mathematics · #51-01 #Differential Geometry (math.DG) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1502.07671
openalex publication_date 2015/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.