Supplementary Investigation 10

Tessellations Based on Glide Reflections & Equilateral Triangles

Tool(s) Geometers Sketchpad

Data File(s) si10

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

Tasks

1. Open the file si10 and vary the segment labeled "side of triangle".

2. Next, move one or more of the marked vertices along the perimeter of the propeller-like object. Do the two actions appear to be linked or independent of one another?

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

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