Problem Set 2

(10 points)

#7, 14, 18, 27 on pages 22-23.

Please read chapter 1 of Gallian.

Label a square of paper on both sides (i.e. 8 markings) as Gallian has and physically play with rotations and reflections as you read Gallian chapter 1, so you can get a feel for what's going on. Just to be clear: if a corner is marked P on the front, it should be marked P on the back. Same for all four corners.

Answer the following questions in complete sentences or paragraphs. Be brief.

1. Is D₄ Abelian or not? Explain.

2. Explain geometrically (using your square paper will help) why a reflection followed by a reflection is a rotation in for this shape. Do you think this holds for any 2-dimensional regular polygon? Why or why not?

2. How does Gallian's use of the word "symmetry" compare with whatever take on the word you had before?�

Come up with a couple of explicit questions or comments on what you found interesting or confusing. Write them down.