Last night we printed a shape from Henry Segerman’s new 3d printing book Visualizing Mathematics with 3D Printing:. We’ve done many project based on Segerman’s work and even were lucky enough to be able to attend his talk at MIT earlier this fall:

The shape we printed last night is Henry’s 3d representation of the 5-cell – a 4 dimensional “platonic solid” ( You can read more about the shape here: The Wikipedia page for the 5-cell)

If you search “Segerman” in the blog you’ll find more than 10 projects we’ve done based on his work!

I started off the project today by asking my younger son for some thoughts on the 5-cell:

One interesting thing that he remembered is that he’d seen the shape previously in some of our bubble projects, so we brought out the bubble solution to make the shape out of bubbles. It was really interesting to hear how he viewed the two shapes differently.

Sorry for the absolutely awful camera work in this video – you’d think I’d have gotten the hang of this after 4,000 videos . . . . .

# A challenge relating to a few problems giving my son trouble

I’ve seen some interesting ideas from Tracy Johnston Zager over the last week about the relationship between learning math and intuition. For example:

Although I’ve been traveling a bit for work this week the relationship between learning math and intuition has stayed in my head. Sometimes my thoughts have drifted to and old blog post about a problem from the European Girls’ Math Olympaid:

A Challenge / Plea to math folks

That post, in turn, was inspired by an old post by Tim Gowers where he “live blogged” his work while he solved a problem from the International Mathematics Olympiad.

It can be really hard for anyone to know what math intuition looks like because everyone sees polished solutions way more often than they see the actual process of doing math.

That’s part of the reason I make the “what a kid learning math can look like” posts – so everyone can see that the path kids (or anyone!) actually takes to the solution of a problem is hardly ever a straight line:

Our “what a kid learning math can look like” series

The other thing on my mind this week has been some old AMC 10 problems that have really given my older son some trouble. These are pretty challenging problems and require quite a bit of mathematical intuition to solve.

So, I’d like to make the same challenge with these problems that I made with the problem from the European Girls’ Math Olympiad – “live blog” yourself solving one of these problems. Post the though process rather than a perfect solution. Let people see *where* your mathematical intuition came into play.