Topologists at play -- the game of Sprouts

It's important to have students think deeply about math in both structured and unstructured ways (I have a guilty feeling that I ought to say more about this, but that will have to wait for a future post). It's the unstructured part that tends to cause problems. That's one of the reasons I liked to make games part of my lessons when I was a teacher.

Games (at least the kind I recommend) require a great deal of focus -- you have to think about what you're doing or you won't do well -- and they encourage exploration and a playful attitude to the material. All of these things help build mathematical intuition.

On the subject of topology, my game of choice is Sprouts, invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967 (as a general rule, you can't go wrong with a game if Conway had anything to do with it).

The rules are simple:

1. Start with some dots on the paper. The more dots you have the longer the game takes so you will probably just want to start with two or three.

2. Players take turns either connecting two of the dots with lines or drawing a line that loops back and connects a dot with itself.

3. The lines can be straight or curved but they can’t cross themselves or any other lines.

4. Each dot can have at most three lines connecting it.

5. When you draw a line put a new dot in the middle.

6. The first player who can’t draw a line loses.

You can find a couple of sample games here.