Last week Kelsey Houston-Edwards published a fantastic video about hypercubes – it is one of the best math videos I’ve ever seen:

Here’s our project on her video:

Kelsey Houston-Edwards’s hypercube video is incredible!

Today while the kids were at school I wrote a couple of Mathematica functions to replicate her results. Writing the code to make these shapes is actually a pretty fun exercise in linear algebra and trig, but that’s a little more than I felt like sharing with the kids just now š

Instead I had them look at the shapes on the screen and tell me what they thought. The first video in each with each kid shows the shape made by a plane intersecting a 3d cube standing on its corners. The second video shows the 3d intersection of a hyperplane perpendicular to the long diagonal of a 4d cube intersecting that cube.

Here’s what my older son had to say:

(a) The 3d cube being cut by a (slightly thick) plane:

(b) The 4d cube being cut by the hyperplane:

Here’s what my younger son had to say:

(a) The 3d cube being cut by a (slightly thick) plane:

(b) The 4d cube being cut by the hyperplane:

This project was really fun, and, as I mentioned above, would also be a great programming project for kids learning linear algebra and trig. I’m 3d printing some of the shapes how, so playing with those shapes will be our project tomorrow!

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