Fractal Folds

Background

Sierpinski Gasket

The last construction is a model of the Sierpinski gasket.

Start with a filled-in equilateral triangle.

Connect the midpoints of each side, dividing the triangle into four smaller equilateral triangles.

Remove the middle triangle.

Repeat on all filled-in triangles.

After infinitely many iterations, the limiting shape is the (equilateral) Sirepinski gasket. Our paper example will realize only finitely many iterates, of course.

The initial triangle and the first three stages of the Sierpinski triangle.

Interesting questions to consider are about finding the area and perimeter of the triangle. After making the paper model, the question of volume can be addressed.

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