Unit 4: The mathematics of art:  from sona drawings to strip patterns November 5 - November 19

 Topic Book Pages Sona drawings handout Traceable graphs class notes web article Rigid symmetries handout Strip patterns AC MMC 177-189 149-157

Book codes:  AC=Africa Counts;  MMC=Multicultural Math Classroom;  CP=Crest of the Peacock;  UHN=Universal History of Numbers

Assignment #4.  (due Thursday, November 29th)

1. Draw the 3x8 and the 6x8 plaited-mat sona.
2. How many lines are needed to trace the following plaited-mat sona?
1. 13 x 26
2. 100 x 105
3. n x 3n , where n is any positive integer.
3. Which of the figures below are traceable and why?  Can you start anywhere, or is there a specific starting point?

4. The figures below represent a lioness and her two cubs;  the right-hand figure is a reconstruction of the left-hand one based on what we know about sona.  What is the largest portion of the right-hand figure that can be traced?  How many lines total are needed to trace the right-hand figure?

5. Identify all symmetries of the following artifacts.  If the object has an axis or axes of reflection or a rotocenter, identify them.
1. The sona drawings in question #3.
2. The sona drawing in Africa Counts, p. 292.
3. The masks in Africa Counts, p. 186.
4. The mbolo (interlacing knot) pattern in Africa Counts, p. 108.
5. The bao game board in Africa Counts, p. 129.  Bao is a game similar to mankala.
6. Identify the symmetry type of the six border patterns in The Multicultural Math Classroom, Figure 9-3, p. 150.
7. Draw a motif that has no symmetries of its own and use it to generate the 7 strip patterns.  You may cut your motif out of paper and trace around it if you wish.

Sample Test Questions.

You may bring a 5x7 index card with any notes you wish on it.  The test will be about 30 minutes long.

• Several questions will be similar to homework questions.  In particular, you should be able to
• determine whether a sona drawing is traceable and give reasons for your answer.
• if a sona  is traceable, indicate how to trace it.
• draw a plaited-mat design of any given dimensions, and determine how many lines are needed.
• find the symmetries of a design.
• identify the seven strip pattern types.
• use a motif to generate a strip pattern of given type.
• There will be a few multiple-choice questions based on lectures and readings.  To help you focus, here are some key concepts we have discussed or will discuss:
• sona  drawing
• graph
• vertex
• edge
• traceable graph
• degree of a vertex
• odd or even vertex
• plaited-mat design
• greatest common divisor
• relatively prime
• rigid symmetry
• reflection
• axis
• rotation
• rotocenter
• translation
• glide reflection
• strip pattern
You should be familiar with each concept and able to give an example for each.

Web Resources.

Images are from the MacTutor History of Mathematics Archive (used by permission).

Rachel W. Hall / Department of Math and Computer Science / St. Joseph's University / rhall@sju.edu