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 Mathematics for Elementary Teachers: An Activity Approach, 8/e
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 Motions in GeometryDrawing Escher-Type Tessellations

# Math Investigations

 Laboratory Investigation 11.2Tessellations 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. (2.0K) Step 2 Rotate the curve about point B so that A maps to C. (2.0K) 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. (2.0K) Once the lines of the original figure have been erased, the figure that remains will tessellate. Starting Points for InvestigationsIf the preceding figure is used to form a tessellation, which of the transformations (rotation, translation, reflection) will map the preceding tessellation onto itself? 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? 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 informationGSP file--Investigation 11.2: Tessellations (15.0K)

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