Starting with an equilateral triangle, we can create a complicated figure by repeating this procedure recursively:

Divide each side of the figure into thirds. Using each middle third as a base, draw an equilateral triangle on each side of the figure. Then, erase each middle third.

Below, you can see the first few iterations of the procedure:

What would the figure look like after infinitely many iterations? We canâ€™t actually draw it, but we are able to compute its perimeter and area. The results may surprise you!

To see our calculations, keep reading. Or, skip to todayâ€™s challenge for a related figure.