math them

I've been making tensegrity polyhedra for about a decade now and have never taken the time to write about them for a general audience, so thought this might be a good time to do so. As with my post on modular origami with Sonobe units , we'll be looking at a single unit along with some mathematical insights that lead to a variety of structures.

When I was a grad student, I used to keep a basket of burr puzzles on my coffee table for guests to fiddle with. Today we'll look at an activity where students design them before solving them!

I've run packing activities before on gridded paper. While it was passable, there were usually a lot of questions about whether objects were successfully packed or peeking out over the line. Here we'll look at an arts and crafts project that serves as a preamble to exploring packing problems.

I volunteered at an event for SUMM the other week where students were putting together different three-dimensional shapes (polyhedra, cylinders, cones, etc) from paper nets . Seeing kids building cones reminded me of sphericons. I hadn't designed a sphericon net before and thought it might make for a fun, slightly-more-advanced build.

I got a couple construction toys and thought I'd look at some things that can be built with them, focusing on loops and polyhedral structures.

Polygon dissections have been a source of amusement and wonder in recreational mathematics for centuries. Today we'll look at a few related activity threads.

I'm in New Jersey this week, so thought I'd break format and give an update on a couple of topics that connect to the trip!

It's tough coming up with a good activity that deals with numbers or geometry in a continuous way, since it usually requires a good amount of prerequisite knowledge. Today's activity is a set of discrete puzzles inspired by a continuous result colloquially known as the ham sandwich theorem.

As summer approaches, JRMF's plan is to develop a slew of activities to test in the fall. To that end, I'll be trying to post activities more frequently but with less of a mathematical dive. Today we'll look at some puzzles involving making polyhedra from a set of faces.

Glen Whitney and Alex Kontorovich are putting together a mathematical art expo visualizing Euler's formula for polyhedra, with polyhedra placed at their respective \( (v,e,f) \)-coordinates to form the plane \( v-e+f = 2 \) in 3-space. I thought we would look at another polyhedron construction method and hopefully end with something we can ship their way!

The other month, I volunteered at Seattle Universal Math Museum's corner of Free First Thursdays at the Museum of Flight. Part of this was helping kids make origami paper airplanes, which reminded me of some origami challenges I used to give students. I'll present one of my favorite arcs here.

My colleague Gabriella Pinter presented a neat 2D rigidity activity at JMM this January that I might write about later, but it reminded me of a 3D rigidity exploration that I've enjoyed running over the years.

I try to design activities every once in a while that have a tie-in to another discipline. Here we'll look at a collection of puzzles that are superficially about words but are more about geometry and arithmetic once you start looking for strategies.