Using 3d printing to share 4-dimensional spheres with kids

A few weeks back we did a project on 4-dimensional spheres intersecting a different sorts of 3d worlds:

What if Flatland wasn’t a plane!

Last night I got around to 3d printing some of the shapes from that project:

Today we talked through the idea of how objects from higher dimensions “look” as they pass through lower dimensional shapes. We started by talking about the idea from Flatland – a 3d sphere passing through a 2d plane. After that we moved on to talking about what the intersections would look like if the sphere was passing through a plane that was creased in to a “V” shape:

Next we moved on to talking about a 4d sphere intersecting the same sorts of objects – a flat 3d space and a “V” shaped one. To create the “V” shape, I just assumed that the 4th dimension – call it w – had a value equal to the absolute value of the x-coordinate.

Next we looked at the 3d printed shapes I made last night. These shapes show a few different stages of a 4-d sphere passing through the “V” shaped 3 dimensional space:

Finally, rather than looking at 4d sphere passing through a “V” shaped 3d space, we went and looked at the shapes made when a 4d sphere passes through a 3d space that is bent like a parabola. So, using my language from above, the 4th coordinate in the space, w, is set equal to x^2.

The shapes here are really cool and also pretty surprising.

Our second facets project

We did this about a week ago and I never got around to publishing it. Both kids are sick today so it seemed like a good day to revisit the old movies.

Our first projects with our Facet set is here:

Our Facets have arrived!

The kids have enjoyed making little creations with the Facets ever since.

Here’s how their 2nd projects looked – my younger son went first. It is so fun to hear a week later how many different topics we covered in the talk about the ring he made:

Here’s my older son’s work. He made an interesting shape that we tried to extend with the camera off. Unfortunately that shape was too heavy for the magnets and collapsed. We got a little lucky, though, and some interesting shapes survived the collapse and we turned them into new, fun shapes:

I’m really happy with the Facets and can’t wait to do more projects with them!