Impulse Gauss Curvatures

In Riemannian (differential) geometry, the differences between Euclidean geometry, elliptic geometry, and hyperbolic geometry are understood in terms of curvature. I think Gauss and Riemann captured the essence of geometry in their studies of surfaces and manifolds, and their point of view is spectacularly illuminating. Unfortunately, curvature is highly non-trivial to work with. I will talk about a more accessible version of curvature that dates back to Descartes