A Surprising Appearance of Euler's Famous Formula: V- E + F = 2

For a convex polyhedron, its count of vertices V, count of edges E, count of faces F satisfy V-E+F = 2. In the "How Round of a Cube?" video ( • How Round is a Cube? (... ) we showed that this equals the "total pointiness" of the polyhedron - surprising! In this video I explore another surprising interpretation of the famous equation.
This video is long. (Sorry!) Here's its breakdown:
00:10 : A Charming School-Geometry Problem in 2 Dimensions: Pushing it to other dimensions.
06:45 Proving the 2-D Puzzle.
FEEL FREE TO STOP HERE
10:17 Making Sense of the 3-D Version of Things.
16:57 On the Areas of Spherical Polygons
24:58 Bringing it All Together

[@12jgy]

Oh my god, this is wonderful, simply mind blowing! It was quite the surprise when Euler's Formula just appeared out of the blue! I found this channel through the MegaFavNumber colab and I was taken by the cheerful enthusiasm of the presentation, it's really quite contagious, and this video is no exception. My mood was kinda down, but this video managed to pick it right back up, so thank you!

[@gucker]

Wow, this is grand! Thank you very much!

[@nikolausbarlow267]

i watched all of the exploding dots lessons exeped the lesson 10 part 2.

[@geraldillo]

Very nice

[@nikolausbarlow267]

i like your 3-d shapes

[@oldreddragon1579]

If a Torus has an inner dimension (hole) of 0 is it

[@nikolausbarlow267]

the 3 d shapes are good.

[@nikolausbarlow267]

noice.

[@Happy_Abe]

Am I color Blind or did green become yellow?

[@nikolausbarlow267]

ether way its guood.

[@nikolausbarlow267]

i mean.. exept

[@nikolausbarlow267]

or nice.

[@nikolausbarlow267]

crona virus