This morning I asked my son to flip through Martin Gardner’s The Colossal Book of Mathematics and pick out a chapter he thought would be interesting to talk through. One of the chapters had a discussion of the Koch snowflake that caught his eye.

Here’s that chapter and why he thought it was interesting:

For today we decided to explore the perimeter to see if we could figure out why it was infinite. For starters we tried to calculate the perimeter of the first four iterations. He had a little trouble with the 4th, but I think that trouble shows why this is such a great arithmetic exercise for kids:

Next we went back to look more carefully at the 4th step to make sure that we had the right number. With this review we found the correct perimeter.

For the last step we found the pattern for how the perimeter changed at each step. This was, unfortunately, slightly rushed as we were about to run out of memory in the camera. But still, I thought my son gave a nice explanation of why the perimeter eventually went to infinity.