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Very few rotations will take the strip to itself.
- Where can the center of rotation be if
the rotation takes the strip to itself? If the center is not in
the middle of the strip, think about a circle through that center
just touching one edge of the strip but not the other. What happens
under the rotation to points near that circle?
- Suppose the center of rotation is
on the midline y=0. What angles of rotation are possible if all
points of the strip are to go to points on the strip? Think
about points near a circle just touching both edges of the strip.