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Differential Geometry: The Intrinsic Point of View

#SoME3 Chapters: 0:00 Intro 2:19 How much does a curve ... curve? 3:56 Gaussian Curvature 7:14 Local Isometries 7:38 The Punchline 8:25 Intrinsic vs. Extrinsic 9:40 How does this apply to us? By explaining the contents of Gauss' Theorema Egregium, I provide an overview of the "intrinsic point of view" in differential geometry: that is, from the point of view of living on a surface (or a manifold, more generally). I compare this point of view to that of a flatlander. Ultimately, this point of view applies more to our existence than we may think...