The Sierpinski Triangle

The Sierpinski TriangleStep One Draw an equilateral triangle with sides of 2 triangle lengths each. Connect the midpoints of each side. How many equilateral triangles do you now have? Image Shade out the triangle in the center. Think of this as cutting a hole in the triangle. Image Step Two Draw another equilateral triangle with sides of 4 triangle lengths each. Connect the midpoints of the sides and shade the triangle in the center as before. Notice the three small triangles that also need to be shaded out in each of the three triangles on each corner – three more holes. Image Step Three Draw an equilateral triangle with sides of 8 triangle lengths each. Follow the same procedure as before, making sure to follow the shading pattern. You will have 1 large, 3 medium, and 9 small triangles shaded. Image Step Four How about doing this one on a poster board? Follow the above pattern and complete the Sierpinski Triangle. Use your artistic creativity and shade the triangles in interesting color patterns. Does your figure look like this one? Then you are correct! Image

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