Not-so-Curvy Curves on Not-so-Curvy Surfaces: Understanding the Gauss-Bonnet Theorem
Here's another deep-dive into some mathematics: an exploration of the "bendiness" of paths you draw in the plane and how their total bendiness changes if you start drawing paths on bent surfaces! Woohoo! 06:00 Kinks and Bends and the Total Bendiness of a Path 04:05 Understanding Flat Geometry 10:01 Paths on a Cube 15:19 The Pointiness of Polyhedral Corners 18:30 The Gauss-Bonnet Theorem for Polygonal Paths on Polyhedra 39:24 Some Concrete Examples 45:37 The General Gauss-Bonnet Theorem 51:28 Sphere-like Polyhedra and V-E+F It's a long one again. Sorry!
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