# Federico Ardila’s “Combinatorics and Higher Dimensions” video is incredible

Yesterday Numberphile published an absolutely amazing new video with Federico Ardila:

The video blew me away – it felt like such a great way to share ideas about higher dimensions with kids.

This morning I shared the video with my older son (my younger son had some school homework that he forgot to do . . . ). Here are his thoughts after seeing the video. One surprise (to me) is that he thought this way of thinking about subsets only works for small sets.

Next I had him label the corners of a cube using the method that Ardila discusses in the Numberphile video. Sorry that the labels on the tape didn’t show up so well, but I think the idea still comes through:

Next – we talked about two versions of the hypercube that we’ve looked at in the past. Then I asked him to pick one of those hypercubes and label the verticies using the ideas from the Numberphile video. I really believe that Ardila’s idea lets kids experience a 4 dimensional cube in a completely new way:

If you know kids who are interested in understanding the 4th dimension, have them watch and they play around with Ardila’s video. It is completely amazing!

The “standing a cube on a corner” ideas we talked about in the 2nd and 3rd videos come from this video from Kelsey Houston-Edwards. Here’s her video and the two projects that we did from it – using the ideas from her video in combination with the ideas in Ardila’s video give kids an amazing look at the 4th dimension

Kelsey Houston-Edwards’s hypercube video is incredible

One more look at the hypercube