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Mathematics for Elementary Teachers: An Activity Approach, 8/e
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Motions in Geometry
Drawing Escher-Type Tessellations
Mathematics for Elementary Teachers: A Conceptual Approach

Math Investigations

Laboratory Investigation 11.2

Tessellations
The following steps illustrate a method of altering the sides of an equilateral triangle to obtain a non polygonal figure that will tessellate. These steps can be carried out with pencil and paper or by computer software programs. Step 1 Draw a curve from A to B.

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Step 2 Rotate the curve about point B so that A maps to C.

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Step 3 Label the midpoint of as D, and draw a curve from D to C. Rotate this curve about D so that C maps to A.

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Once the lines of the original figure have been erased, the figure that remains will tessellate.

Starting Points for Investigations

  1. If the preceding figure is used to form a tessellation, which of the transformations (rotation, translation, reflection) will map the preceding tessellation onto itself?
  2. Step 3 produces a curve on one side of the triangle that is said to have point symmetry because it can be rotated onto itself by a 180˚ rotation. Suppose Step 3 is used to produce a curve with point symmetry on all three sides of a triangle. Will the resulting figure tessellate?
  3. Suppose Step 3 is used to create a curve with point symmetry on each of the six sides of a regular hexagon. Will the resulting figure tessellate?

Tessellations Investigation (Chapter 11, Section 2)
Read Me - Tessellations Instructions (Word Format) (35.0K)

Click on Geometer's Sketchpad in the left menu for information
GSP file--Investigation 11.2: Tessellations (15.0K)