Antelape on a 3 × 4 grid of dots
Figure 9a
Source: Peulus Gerdes, Desenhos da Africa
Imagine that there are no schools of the kind you attend. How do children learn? Who teaches them? Before most children went to school, they were taught by their parents and by the older people of their society.
The Chokwe people live in north eastern Angola, a country in southwestern Africa. They are mainly farmers, but they also hunt animals for food. Before the days of radio and television, before the time of schools, children would gather around an old person in the evening, after the work was done. They would sit around a campfire or under the shade of a tree and learn about their history, how to get along with people, and how animals behaved.
The Chokwe people are known for their wonderful art. They decorate the walls of their homes with interesting designs. When the elder tells a story, he draws a picture in the soil to make the story come alive. First he makes a grid of dots, then he traces a design between the dots while telling the story. These designs are called sona; one design is a lusona. Usually he draws the lusona without taking his finger off the soil or pausing in the storytelling.
Today we will talk about and draw two animals: an antelope, and the path of a wild chicken as it is chased by a hunter.
• Several sheets of graph paper (use lined paper if you don’t have graph paper)
• Pencil
• Eraser
• Colored pens
• Ruler or straightedge
1. On the graph paper draw a 3 × 4 grid of dots to form a rectangle. Hold the paper so that the lines run diagonally.
2. With your pencil, start the drawing on the left side, between the 2nd and 3rd row. Draw your lines through the intersections of the graph paper lines, the points where the lines cross. You may want to use a ruler to draw straight lines. Figure 9b
3. Continue to draw the body of the antelope without lifting your pencil off the paper. Draw each line until it reaches the turning point, just past the last dot in the row or column. Figure 9c
4. Add the head, legs, and tail to the body.
5. Go over the lines with a colored pen.
Does your antelope look like Figure 9a?
Figure 9b
Body of the antelope
Figure 9c
Look at the path of the chicken as the hunter is chasing it. It makes some sharp turns, almost retracing its path. Figure 10a
1. Draw a 4 } 3 grid of points on graph paper. Skip an intersection between each pair of dots.
2. With your pencil start drawing in the lower left and continue as in Figure 10b Try to do the whole drawing without taking your pencil off the paper. Figure 10b
3. Complete the path of the chicken. It finally comes back to the starting point.
4. Go over the drawing with a colored pen. Does it look like Figure 10a
1. Look at the drawing of the body of the antelope in Figure 9c. Does it have a line of symmetry? Can you fold the paper on a line so that one half fits over the other half of the drawing? How many different lines of symmetry can you find? Can you rotate (turn) the paper so that the drawing will look the same in a different position? In how many different positions does the drawing look the same?
2. Look at the drawing of the chased chicken. Does it have line symmetry? Does it have turn symmetry?
You may find answers on page 154.
Path of a chicken as it is chased
Figure 10a
Figure 10b
Here is another drawing of the path of a chicken as it is hunted down. This chicken led the hunter on a merry chase!
Take a thin sheet of paper and lay it over the diagram. Fasten it down with paper clips so that it doesn’t move. Then try to trace the whole drawing without lifting your pencil off the paper. You may start any place, and you should end at the starting point.
After you have traced the diagram, try to draw it on a 6 × 5 grid of points.
Dr. Paulus Gerdes is a mathematician living in Mozambique. Both his country and Angola are former colonies of Portugal, as is Brazil, in South America. Dr. Gerdes has written several books about the sona of Angola. One book, published in Brazil, is for children (see the Bibliography on page 157). It is in Portuguese, the language spoken in Brazil. I hope the book will be translated into English.
Path of a chicken as it is chased
Figure 11
