Lab, Wed 11/18

1. Illustrate the double-reflection = rotation or translation thm.
2. If you feel unsure about this, create a sketch and see how it works by measuring angles, etc.

3. Product of rotations.
4. This is the theorem done in class today that is also Thm. 11.1 in Bix. Do this construction with Sketchpad and transform a shape or a point by the product of rotations and see that the product is what it is supposed to be.

5. Investigate products.
6. Do the problems in Bix 9.21 using the ideas of 2 above.

7. Pattern generated by a line reflection and a translation.
8. Let M be a line reflection and T be a translation. Investigate the product TM in the special case when T is perpendicular to the mirror line of M and in general.

Also, take blob and generate a pattern by repeated applications of T and M.

9. Look at the files on the server made with mirrors and explain the rotations you see there.
10. Generate a pattern with R = rotation by 90 degrees with center A and a line reflection M with mirror line m not passing through A.

7. Generate a pattern with R = rotation by 90 degrees with center A and also S rotation by 90 degrees with center B.