Summer of Math Exposition

How Many Symmetries Are There

Explains how to calculate the number of possible symmetries spherical, wallpaper, and frieze symmetries. Uses a clever argument based on orbifolds and the Euler Map Theorem. The argument is based on a book called the Symmetry of Things. The argument is very visual. This animation illustrates concepts that are hard to present in book format. The illustrations and animations are all original.

Analytics

7 Overall score*
45 Votes
16 Comments
Rank 8

Comments

Beautiful!

7

Exceptional animation and explanatory pace. Not super novel, and at its worst felt like you were just saying facts. But overall great.

7.7

You were a little bit naughty dividing by infinity though

7.1

the video explains the concept pretty well and the motivation behind video, it explains the concepts pretty well for someone who never studied that and the examples at the end are really cool to show how that stuff is useful in a practical manner but i hoped he would talk a bit more about that but overall its a really good explainer

8.2

Well-made animations and a properly thought out structure. Overall a very solid video

7.7

The topic was very interesting, but it was hard to follow the arguments. I think there were too much stuff in the video. Would prefer less content but more time spent on the explanation.

5.9

Goal Orientation: 4/10 Novelty: 1/10 Thought-Provoking: 2/10 Comprehensibility: 6/10 Technological: 6/10 Overall Average: 3.8/10

4.2

This is so wonderful and clear.

8.9

I undeestood how symmetrical like 2*3 work, but later you started using multiple numbers (like *3333), loosing me on what those symmetries mean. I think you jumped into the thick of things a but quickly. Interesting video, though!

3.1

This was a really good explanation. The video and the animations are good, but I feel like everything was a bit monotonous. A bit more explanation would have been appreciated in the beginning, on why and how the reflections and rotations are the way they are on these balls. But, again, good video overall!

4.8

I would like to thank the author for adding a source reference! I really appreciate when videos presenting a topic do that, as I can then look up the book and delve into the technicalities of it, after having digested a thoroughly explained video.

9

Beautiful animations, well explained, John Conway, what more can we ask for?

8.7

The animations are very nice. The video rushes through the material too quickly and it becomes confusing.

5.5

I like this animated overview for Part I of Symmetries of Things. After my first viewing, I paused often during replays to digest ideas, e.g., the 2D embeddings onto a sphere as a guide to the book's table of "costs". I wish the narration included comments about changes to level of detail: lots for octants of basketball, blurred soccerballs (00:10, 00:16, 01:23), discussion of miracle & wonder, brief displays of various annotated triangle or rectangle superimposed on wallpaper. Your overview of notation involves identified patterns; it does not address the issue of completeness - have all symmetries been identified (e.g. stop at *5 or *53 for a soccerball)?, are the announced categories independent?

7.2

Very nice visuals and animations if there was some music, it would be outstanding.

8.2

excellent animation supported exposition, if i could suggest anything it would to narrate with more breaks or talk through the notations but not over the animations?

4.8