(ma[th)em]: a JRMF activities blog

Today we'll look at an activity that explores different aspects of expressing a positive integer as a sum of squares.

I've been toying with some potential activities that involve division. Today we'll look at an activity that makes heavy use of division and partitions, skinned as a factory trying to make as many nanobots as possible.

Rubik's cubes have a strange place in our pop culture as artifacts that only geniuses can solve, but the many guides on solving them have made solution techniques pretty accessible to a wide audience. Mathematicians like them because they provide a shiny introduction to group theory that leave students with a neat party trick. Today we'll look at the "pocket cube" (the 2x2x2 version, typically abbreviated 2x2), which I've had good luck introducing to beginners.

As our community math circle prepares to run Magic Flowers, I've been looking at extensions and related problems. Here we'll look at a series of puzzles that also require certain sums to be the same.

Gord Hamilton's Kickstarter for The Infinite Pickle is very close to meeting its goal, so I thought today we'd look at a small corner of Boring Conversations , an activity from this collection that was presented this week at the Math Incubator workshop.

My colleague, Daniel Kline, was looking at chain linking manipulative and wondering what activities could make use of them. While he's working on an activity based on symmetries, I thought I would write one up based on de Bruijn sequences.

When JRMF throws a festival, some activities will invariably be more popular than others. When we introduce enough new activities, some old ones stop stacking up against the rest. While a new activity eclipsing an old one isn't a terrible problem to have, Ladybugs is currently not a fan favorite, and it is one of our more outwardly arithmetical activities. Since having a few arithmetic-forward activities in the bunch make it easier to sell our offerings as mathematical to the skeptical, we'll take a look at it as it stands and consider a reimagining.

Here we'll look at some topological puzzles originally cast in terms of hanging a picture frame.

Combinatorial game theory is a deep well to draw from in the math enrichment world. JRMF has Apple Picking , Countdown , Rook's Move , and Sprigs on the books. I thought we'd look at the classic Grundy's Game and a few variations. I'll take this as an opportunity to introduce a few concepts useful in analyzing combinatorial games, more broadly.

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!