Triangle Subdivision - Numberphile

Featuring Professor Volkmar Welker from Philipps-Universität Marburg.
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran
Animation by Pete McPartlan
Thanks to the Numberphile Society, especially CJ Smith!

[daniellambert]

I'm always amazed by the types of questions Brady asks the subject matter expert. It really helps ground the topic, and dig a little deeper than the presenter would have normally delved.

[fruity]

Brady has a great talent for asking the question his viewers might be asking. Whenever I have a question I would have asked if I was in the room, Brady asked it a few seconds later, as if he can hear it, it makes the videos almost as great as hearing the conversation in person

[andrewgries]

Nothing like starting your morning with a big cup of triangle subdivision.

[DanDart]

I love how active in the conversation Brady has gotten over the years. He's asking so much and helping us all learn so much.

[QuantumHistorian]

Brady doing the heavy lifting of the explanation here by asking all the right questions!

[jadenpeterson]

Wish I knew this back in math class when I got caught doodling. “No teacher, I’m not doodling in the margins, I’m just practicing my polygon subdivisions.”

[zacgarcia]

It's weird seeing stuff I used to doodle in school actually be a mathematical concept

[Tatterdemalion-]

This is oddly satisfying. I may not fully grasp it, just love that people are out there doing these things, just for the pure love of mathematics, I don’t need applications.

[tuckerleavitt]

Next time I'm playing a 4d video game I'll thank Dr. Welker for working out all the tetrahedral meshes

[G.Aaron.Fisher]

"We connect two vertices if the corresponding faces are contained in each other."

Even with the previous definition of faces that was glossed over, this is surprisingly imprecise and difficult to parse. I don't know how anyone could understand what's going on if they watched this video at full speed.

[mattp]

If at first you don't succeed in inventing a new subdivision rule, tri, tri again.

[deliciousrose]

I love how Brady always know what question will be asked by viewers

[ShadwSix]

Kudos to the 3D modeler and animator for helping us visualize the subdivisions. Thank you.

[Marconius]

I've used these before in 3D modeling, very useful when you want to essentially increase the resolution of your model without changing its shape. Though I will point out that just dividing flat triangle surfaces will only ever give you a flat result, so this alone won't actually make your model smoother or something... there are other methods for that though.

[paoloangella]

OMG I had a course with him in Erasmus! Great guy!

[toferg.]

Y’all make a great team. It couldn’t have been achieved with only one of you.

[FloydMaxwell]

Cool computer graphics to go with the presentation of the theory

[ounayec]

Fun fact : You have link between the subdivision of simplexe and distributed computing, you have to make a Schelgel Subdivision and then associate a combinatoric interpretation of it. Another way to said it is : their is a way to subdivide triangle to obtain every pre-order possible between d variables ( for pre-order with 3 (or d) variables you start with the simplexe of dim 2 (or d-1)). The key word is Chromatic Subdivision have fun !

[lordofmorgul]

What a cool name - Volkmar.

Volkmar - The Dark Lord of Triangles!

[EebstertheGreat]

I wonder what a Parker subdivision would be. Maybe it would have a double-edge or double-vertex. Maybe it would have a point labeled (-1, 0, 1) or something else not allowed. Maybe it would have a quadrilateral hidden in there. I can't decide.