In the applet below, use the mouse as a brush to draw a picture. Describe the pictures you get. Can you see any evidence of rotations?
Notice that every brush stroke gives you three images except at one place -- find the location where you only get one image (the fixed point). If you rotate the picture with that point as the center of rotation through an angle of 120°, 240°, or 360°, you get the same picture. We say that your picture has rotation symmetry of order 3.
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