Now all this has, as promised, a number of surprising connections. The first is to those childhood favorites-- paperdolls! We need to explain the rules:
Given a pattern, try to arrange the paper into a carefully designed wad, cut a design through all the layers, and unfold to find a design with the desired symmetry.
Click here to get some paperdoll masters. Here are some more!
You can also use all kinds of stuff-- Escher prints, your own kali printouts, the Frieze! sheet, or whatever!
CAUTION: As you cut, make your design lopsided, so you can tell you're getting the right symmetry; also remember-- you have to cut all the way through!
Q10: What is the method for producing each of the desired symmetries? In particular, what form must you wad the paper up into for each symmetry? Sketch the symmetry and sketch the wadding-method needed for that symmetry.
Now you don't want to spoil the surprise, so wait until you're ready to go on to
A really cool connection!
Chaim Goodman-Strauss Dept. Mathematics Univ. Arkansas Fayetteville, AR 72701 firstname.lastname@example.org 501-575-6332