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.

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.

Today we're going to look at some arts and crafts projects related to great (and not-so-great) circles found on polyhedra and links. A few of these models were shown to me by Mircea Draghicescu of ITSHPUN fame and the rest are riffing on the theme.

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!

There are a number of activities based on Möbius bands in recreational mathematics lore. Here we'll look at a variant with some topological and number sequence aspects.

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.