Computing the area of a Koch snowflake

Yesterday my younger son and I explored the perimeter of the Koch snowflake. He was surprised that the perimeter was infinite, but he also thought that the area was finite. Today we calculated the area.

I started off by asking my son for a plan for how we should approach the problem:

In the last video we calculated the additional area that was added in each step of the process of creating the Koch snowflake. Here we look carefully at those amounts and take a guess at the pattern.

Now that we had the pattern, we added up all of the areas. I really enjoyed seeing my son’s approach to adding up the infinite series. I think this calculation is a great one to show to kids to sneak in a little arithmetic practice as well as introducing some simple ideas about sums of infinite series.