Inspired by one of my favorite posts ever I sat down with an open notebook and started playing around with hexagons, looking for some interesting math.

(Sitting down with a blank page of notebook of paper and just doing some math was an incredibly rich experience for me, and I’m still coasting off of it. It yielded a lot of good ideas.)

One of the things that I quickly realized, as I was looking for interesting things about hexagons, was that in order to do interesting work I needed a nice variety of hexagons to play around with. Creating a gallery of hexagons was a non-trivial exercise for me.

Creating this gallery and investigating them turned out to be a process with a good deal of positive feedback. Creating shapes yielded interesting ideas, which in turn required the construction of certain types of polygons for investigation. (In particular, as I settled in with inscriptions of polygons I found certain hexagons that persistently showed up. I’ll post this somewhere else soon, but “Lamps” and “Emeralds” seem to switch on and off in the sequence of inscribed polygons.)

Anyway, this is a post to say that I think that I’d like to give kids the chance to poke around with polygons for a while, because I think that it’ll give them a library of examples and counter-examples that will be useful in the sort of investigations that we’ll do throughout the year.

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