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

Readings.
Topic 
Book 
Pages 
Sona drawings 
handout 

Traceable graphs 
class notes
web
article 

Rigid symmetries 
handout 

Strip patterns 
AC
MMC 
177189
149157 
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)

Draw the 3x8 and the 6x8 plaitedmat sona.

How many lines are needed to trace the following plaitedmat sona?

13 x 26

100 x 105

n x 3n , where n is any positive integer.

Which of the figures below are traceable and why? Can you start anywhere,
or is there a specific starting point?

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

Identify all symmetries of the following artifacts. If the object
has an axis or axes of reflection or a rotocenter, identify them.

The sona drawings in question #3.

The sona drawing in Africa Counts, p. 292.

The masks in Africa Counts, p. 186.

The mbolo (interlacing knot) pattern in Africa Counts, p.
108.

The bao game board in Africa Counts, p. 129. Bao
is
a game similar to mankala.

Identify the symmetry type of the six border patterns in The Multicultural
Math Classroom, Figure 93, p. 150.

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 plaitedmat 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 multiplechoice 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

plaitedmat 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.
Multicultural Mathematics
home page.
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