Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

This article gives a proof of the uncountability of the Cantor set.

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

In this article, Rachel Melrose describes what happens when she mixed mathematics with art.