Motions in Geometry
Drawing Escher-Type Tessellations
|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.
Step 2 Rotate the curve about point B so that A maps to C.
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.
Once the lines of the original figure have been erased, the figure that remains
Starting Points for Investigations
Tessellations Investigation (Chapter 11, Section 2)
- If 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?
Read Me - Tessellations Instructions (Word Format)
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GSP file--Investigation 11.2: Tessellations