Having kids play with 4 and 5 dimensonal Hasse diagrams

Yesterday we did a fun project on Hasse diagrams:

https://mikesmathpage.wordpress.com/2020/05/24/exploring-hasse-diagrams-with-kids-thanks-to-martin-weissmans-an-illustrated-theory-of-numbers/

The boys got the hang of a few relatively simple examples but also noticed that going to numbers with 4 prime factors would get pretty hard to draw.

After we finished the project I saw a post on twitter about a 5d cube and was reminded that we had a 2d projection of a 5d cube hanging on our living room wall:

We have the projection of the 5d cube you can make with zometool hanging on our living room wall 🙂 pic.twitter.com/yTVJoJFhjc

— Mike Lawler (@mikeandallie) May 24, 2020

So for a challenge project this morning I had the boys try to figure out how a Hasse diagram would work in 4 dimensions and in 5 dimensions.

Here’s how the 4d case went:

The 5d case was significantly more challenging – but they got there! Here’s the explanation of their work:

Who would have ever thought that a 5d cube appearing in your twitter feed would be exactly the thing you needed to see for a new math project!