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Math and Logic

Stack of Squares

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 can’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 today’s challenge for a related figure.

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