• Step 1: Draw an equilateral triangle ABC.

  • Step 2: Find the midpoints of each side. Connect each midpoint to form three new lines inside of the original triangle.

  • Step 3: Continue to repeat step 2 with each right-side-up triangle.

    Each stage of your triangle should look like those below. The area of the triangle that is shaded is part of the shape and anything not shaded would have been cut-out of the picture.

    Serpinski Triangle Stage 0

    Serpinski Triangle Stage 1

    Serpinski Triangle Stage 2

    Serpinski Triangle Stage 3

    Larger Triangles

    Serpinski Triangle Stage 4

    Stages 0-4

    One important thing to realize about an actual Serpinski Triangle is that it only exists in your mind! That's because you must have done the above steps an infinite number of times. Anything less than this is only part of a Serpinski Triangle.

    Let's find out some things about this triangle. Click on activities.

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