The wall painting on the house in this photo shows geometric transformations: reflections, rotations and translations. The symmetries of a design are the transformations that leave the pattern looking exactly the same.
Assume that the parts of the design that look the same are identical and that they only appear different because of the perspective in the photo. Describe in detail all the transformations and symmetries that you see in the different parts of the painting.
(1) Describe the image of this part of the pattern if it is rotated by 180 degrees about its centre? What about two rotations?
(2) Describe the symmetries that you see in this part of the pattern? What do you notice about the larger part of the design, with this at its centre, surrounded by 4 copies of the design from part (1).
(3) Describe the reflections you see in the strip pattern at the top of the wall.
Click here for a copy of the pictures and here for Notes for Teachers
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