Tool(s) Geometers Sketchpad

Data File(s) si12

Focus A curve is defined from the endpoint to the midpoint of one side of a square. This curve is extended over the second half of the side using a rotation. When the curve is replicated on the other sides of the square, the resulting object tessellates the plane.

Tasks

1. Open the file si12 and vary the segment labeled "side of square" and the positions of one or more of the marked vertices along the perimeter of the object.

2. Measure and compare the areas and perimeters of the objects.

3. State a conjecture based on your observations.

4. To prove your conjecture false, what sort of counter example would be necessary?

5. Create your own version of this file, using more points to define the curve.

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