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Tom Evitts, SU Math Dept.

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Geometric Shape Composed of Self-Similar Parts

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Self-similarity Following directions Iterative steps Creative processes Seeing patterns Math is more than equations... Math is fun!

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You need: Piece of paper Scissors Ruler Fold paper in half (portrait: bottom to top) fold

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Along the fold, measure in and mark ¼ of the distance from each edge.

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From the fold, measure up and mark ½ the distance to the top.

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Use the marks you made to lightly create the lines shown below. Cut along those lines.

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Carefully fold the flap you have cut up inside the folded paper. If you measured carefully, it should just reach the top edge. Concealed flap

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Repeat the iterative sequence (next slide) using the rectangle hiding the concealed flap as the starting object.

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Along the fold, measure in and mark ¼ of the distance from each edge. From the fold, measure up and mark ½ the distance to the top. Use the marks you made to lightly create the lines shown. Cut along those lines.

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Carefully fold the flap you have cut up inside the folded paper. Your cutout should look like this:

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Unfold and examine your fractal cutout. What properties do you observe?

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Repeat the steps with a smaller rectangle. Can you figure out which one?

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Repeat the steps with a smaller rectangle. Can you figure out which one?

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What patterns are you finding? Perform another cutting and folding sequence. What if you could cut and fold “forever?”

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Have a great semester!

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