In Division By Zero’s blog, A Game for Budding Knot Theorists, he introduces the game Entanglement (CAUTION: Entanglement is rather addicting. Proceed with caution and plenty of time to kill). This article stood out to me because I recall Prof. Heath talking about Knot Theory during our last capstone meeting.
The object of the game is to create the longest knot possible. In the blog post itself, however, the upper bound of the length of the knot (a “perfect game” if you will) is discussed. We see that each tile is a hexagon, and thus has six sides. Furthermore, there are 36 tiles in a full board. There are also 48 boundary sides, one of which the knot may go onto. Thus the largest possible knot is 6*36-(48-1)=216-47=169 tiles long. The next logical question is whether or not this is attainable. It turns out that it is (the proof is that someone did it, no mathematics necessary this time).