Directions:  You may work together, but please write your answers in your own words.  Please write (neatly) on one side of the paper, cut off any messy edges, and staple the papers together.

1. Draw any 2 of the following.
1. A leopard with 6 cubs (see p. 220, Fig. 4.42).
2. Trunks of the kajana tree, starting with triangles with 6 dots on each side instead of 5 (see p. 209, Fig. 4.8b).
3. A 5x5 version of the lion's stomach design (see p. 214, Fig 4.22)
4. A resizing of the spider in its cobweb design that's different from the ones shown in p. 215, Fig. 4.24 or Fig 4.25.
5. A flying duck design with 4 ducks that is monolinear and symmetrical.
6. A 4x4 or 5x5 Celtic knot that's similar to the ones on this handout but has a different grid (i.e. a different set of ``mirrors'').  You can read more about knot construction here.
2. The following questions refer to the article ``Knots in chemistry and physics'' on p. 240-245 in your course packet.  There is a lot of mathematical detail here--just try to get a sense of the main ideas.
1. What is the main goal of knot theory?
2. When are two knots equivalent to each other?  (Think about the exercises we did in class, too.)
3. What is the unknot?
4. What is the ``world's smallest knot?'' (as of 1993)
5. What is one surprising fact you learned from this article?
6. Vaughan Jones is the chief mathematician associated with knot theory.  On the Internet or elsewhere, find an interesting fact about Vaughan Jones.  Be sure to cite your source.
3. Take Barry Dayton's interactive strip pattern tutorial.  When you are done, email me the code.
4. Read about sipatsi on p. 248-252.
1. Classify the three strips on p. 250, Fig. 1.1, the strip in Fig. 1.3, and the strip in p. 251, Fig. 1.5, using the pq system.
2. What is the period of the strips in Fig. 1.1?
3. How are common multiples important in sipatsi weaving?
4. What does Fig. 1.9 on p. 252 represent? (I had to laugh!)
5. Read about titja baskets on p. 253-257.  Look at the five photographs on p. 256-7.  What types of symmetries do the baskets have?  Which have reflections?  If they have rotational symmetry, find the degree of the rotation.
6. The article on p. 259-273 is the text of a lecture by the famous Dutch artist M.C. Escher.  You may recognize his designs from T-shirts or posters.  On p. 269 he discusses some of the designs from various cultures that inspired him, pictured in "Eight copies of space-filling designs" above.  Of these eight designs,
1. Which have reflectional symmetry?  Is it horizontal, vertical, or along a diagonal?
2. Which have rotational symmetry of 180 degrees?  Of 90 degrees?  Of 120 degrees?
3. What type of symmetry does Escher's "Swans" on p. 261 illustrate?
7. Extra Credit.  Use the Wallpaper Drawer to make one of the designs shown in the Escher article.  Use Print Screen to print your work.