These are some shapes that a couple of students produced and pondered in my Geometry class today. They’re art galleries that need to be guarded with cameras. This is the Shape problem from Investigation #2: what shapes require what numbers of cameras to guard them?
I love this problem. One reason is how different students come at it from such different angles. Today, one group’s galleries were all pretty boxy, but also kind of intricate. Another group’s galleries all consisted of a single square room, but with wall partitions coming in from the edges to block cameras’ views. And finally, this group started with a circle and then did some squishy (read: topological) transformations to it to explore how many cameras they could force.
The art gallery problem really does a great job of evoking the geometric property of Shape. I think there’s a tendency in Geometry classes to focus to quickly on the “standard” shapes about which classic and easily-proven theorems will be introduced. This Investigation helps to show how wild and wooly the world of shapes can be.
The class is really starting to hit its stride and gel. I’m excited!
Lanier Post-a-Lot 
Such a cool problem. I talked to some kids about it. They were digging it.