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!

[@SalixAlba256]

So good to see Gauss-Bonnet presented in a discrete case. Makes is a more easy to see how it works.

[@AllothTian]

Wonderful presentation, James!

[@tomt8785]

Your enthusiasm is contagious :) a very nice video!

[@AbhijeetVakil]

Love your enthusiasm :)

[@zussini2172]

I must say it is first class presentation, easy to grasp, most of it even to elementary school kids. Maybe I will use some of the ideas. Great

[@pradeepkumaragarwal3863]

Too inspirational for us sir❤️❤️❤️👍

[@matti1610]

Great video!!! Thank you!!

[@frankied.2828]

Hey, I love your presentation!

[@maynardtrendle820]

I wish I could parse that thick Highland Scottish accent. Probably some good maths here. A shame🤷🏼‍♂️

[@magicjim1]

It's a lovely Australian accent.

[@benjaminfink9580]

Pretty easy to understand

[@maynardtrendle820]

@@benjaminfink9580 It was a joke brother.

[@maynardtrendle820]

@@magicjim1 It was a joke my friend.