Summer of Math Exposition

Hypergraphs and Acute Triangles

We solve a problem about acute triangles from the 1970 International Math Olympiad (Problem 6). Moreover, we improve the limiting bound from 70% to 56.15%. The solution uses recent results from the theory of hypergraphs.

Analytics

6.9 Overall score*
33 Votes
11 Comments
Rank 16

Comments

I liked the slide format! Maybe would’ve helped to have a few more detailed visualisations in places, particularly e.g. when describing the construction of tetrahedron-free hyper graphs? Also could’ve linked back to the original problem earlier, perhaps around when you introduce the tetrahedron-free graphs? Some light background music may have helped I liked that you had a clear structure for the video, but you may have telegraphed it a little _too_ much? E.g. saying explicitly that “now I’m going to show…”. I’m not sure, maybe there’s an element of “show, don’t tell” here… It’s great that you had lots of references (though as a judge I don’t exactly have the time to check all of them out), but it did kinda make it harder for the video to stand out on its own. By the way, definitely take everything I say with a massive grain of salt, I don’t like Olympiads or combinatorics too much! And I still felt like I got something interesting out of your video :)

5.9

I consider this to be an outstanding entry. The problem posed is interesting, the background is well-explained and well-illustrated. The pacing is great; the narrative and diction clear and the general tone highly motivational for the viewer/listener (encouraging them to explore the area further). I am most impressed.

9

Whilst the content was interesting to learn about, the video and presentation itself wasn't very engaging and I found some of the explanations a bit difficult to understand.

3.1

Excellent video! I do wish it had included an explanation of the wedge-counting bounds.

8.1

This was an outstanding video! I loved your motivating problem, even though I forgot about it as you were going through the theorems you were going to use. I also especially loved that you covered some of the history of the mathematicians who have worked on these problems; I don't see a lot of that in these sorts of videos and I thought it was really cool and interesting. The math you covered was great, the way you covered it was great, all-around amazing video! Congrats and thank you for making this!!! :)

9

This one was too hard for me, but I really did appreciate the previous one (acute triangles)

7.3

Excellently done! The connection is beautiful

7.6

Goal Orientation: 9/10 (I like the outline) Novelty: 4/10 Thought-Provoking: 8/10 Comprehensibility: 9/10 Technological: 8/10 Overall Average: 7.6/10

7.8

I think that the application of hypergraphs to the acute triangle problems was quite interesting and the overall flow was logical. It built step by step upwards towards how we could solve the initial problem. I think the presentation can be made a bit more concise to help to refocus on example problem as the main goal as there was quite a lot to unpack within a 20-30 min video.

6

motivation 8/10 clarity 7/10 novelty 5/10 memorability 5/10 fantastic entry thank you

4.6

Probably the best math video of my mounth what an amaizing discovery. Everything look's good, the story, the math, the subject (hypergraph)

9