4 dimensional spheres

Last night my older son asked me what a 4-dimensional sphere looked like. We talked about it a little bit last night and I decided to turn the question into our 400th Family Math project (and, sorry for writing 399 in the videos, I sometimes lose track of where we are!).

We started the project today by talking about squares and cubes. Getting up to the hypercube by “sliding” the each shape in a new dimension is the typical way that we’ve discussed 4 dimensions in the past.


Next we talked about circles in 1, 2, and 3 dimensions. The main idea of this part of the project was to have the kids understand what it looks like when an “n+1” dimensional circle is projected down to “n” dimensions. The boys also had some great ideas about how circles in different dimensions related to each other.


In the final part of the project we used the ideas from the last video to understand 4-dimensional spheres. It was fun to hear my younger son describe what he thought the shape would look like.


I’m happy to have had our 400th project come from a question my son, and also happy that it was a topic that both kids could enjoy.

Can’t believe we’ve made it to 400. #1 feels like it was a looooooong time ago 🙂


3 thoughts on “4 dimensional spheres

  1. One of my kids was also really excited about 4d shapes recently. Two good follow-ups to the discussion about slices (from a higher dimensional shape moving through a lower dimensional space):
    (1) are there any other shapes that would give rise to the same pattern of slices (1d from a 2d shape, 2d from a 3d shape, etc)? Yes …
    (2) What do the 3d slices of a tesseract look like? This is nicely illustrated on Matt Parker’s great talk.

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