Рет қаралды 2,166
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!