Summer of Math Exposition

Penrose Tilings from Five Dimensions

This contribution highlights that aperiodic Penrose tilings can be viewed as projections of a periodic five dimensional cubic lattice. We focus on the geometric properties of this projection and try to motivate the choices that are required for a Penrose tiling. To cope with the five-dimensional geometry, lots of toy models and analogies are exploited.

Analytics

7 Overall score*
41 Votes
9 Comments
Rank 7

Comments

One of the best videos I’ve seen in a long time! It’s such a cool way to get to the Penrose tiling!!! And I felt like you made such a good effort to ensure each step felt motivated and that the reader never got too lost, even as you went to higher dimensions. Lots of great humour and very impressive visuals. Only very minor comments - perhaps taking a few more pauses would help, or longer pauses? Honestly sometimes i was just in awe of the presentation and wanted to experience it a bit longer before you moving on. Also, maaaaybe some very light background music? Again these are just nitpicks really, the video was superb!

8.3

I must admit that the topic is far too difficult for me, but I am extremely impressed by the quality and clarity of the visualizations. I will come back to it mater.

9

This is a pretty chunky topic, and one thing that I find helpful for following along is if the voice over has variation in tone and pacing for emphasis on important parts (or for de-emphasis of less important parts).

5.6

Amazing animations!

7.8

lovely stuff motivation 5/10 clarity 5/10 novelty 5/10 memorability 5/10

5.9

interesting butvery difficult to follow

5.8

A very interesting video! Although it's probably more or less impossible to fully understand every little detail on the first watchthrough (unless you really try to pick it apart step-by-step, pausing and rewinding until everything is clear), it's really nice to see how the Penrose tiling can be understood in this way. I enjoyed this one immensely, and the visualizations really helped in highlighting what is going on.

9

Honestly a really really well done entry. Only thing I think could be improved is audio quality, and perhaps brevity.

7

Outstanding! You video deserves to win the competition.

9