Exploring Curvature

. . . one should not be too ready to erect a wall of separation between nature and the human mind. d'Alembert [Dugas (1955)] It is possible to present mathematics in a purely fonnal way, that is to say, without any reference to the physical world. Indeed, in the more advanced parts of abstract algebra and mathematical logic, one can pro­ ceed only in this manner. In other parts of mathematics, especially in Euclidean geometry, calculus, differential equations, and surface ge­ ometry, intimate co