Math 402, Assignment 12, Spring 2008

Due Wed. April 30 (at the beginning of class)

1. Finish the work we began in class by carefully describing what you get when you first rotate about P by alpha degrees and then rotate about Q by beta degrees. Give a detailed answer, for example, if it is a rotation say about what point and by how much. Prove your claim. Make sure that you consider every case.
   
   
2. Consider the following claim: Any two lines which do not intersect must have a common perpendicular.
   1. Prove that the claim holds on E^2.
   2. Prove that, in absolute geometry, PP implies the claim.
      Hint: This should be easy, once you have proved the first part.
   
   
   
3. For each of the types of strip patterns which we described in class, draw an original artwork which has that type of symmetry. Draw in the lines of reflection, the glide lines, and the points of rotation.