Drawings from Angola: Living Mathematics

Drawings from Angola introduces its readers, eight to fourteen year olds and their educators, to a small piece of the culture of the Cokwe people who live in the northeast of Angola. In particular, he focuses on the mathematical thought that can be found in the sand art which accompanies their story telling tradition.

The book opens promisingly with three stories from the Cokwe culture and their accompanying drawings. It then moves on to discuss the patterns and methods of construction for some of the simpler drawings, though not those in the stories. Throughout the text Gerdes continues to introduce new drawings, each time indicating what the drawing represents in a story, though he does not return again to the appealing story-drawing paradigm found at the opening of the book. After the brief initial set of drawing directions the author encourages the reader to attempt a number of similar drawings. He also asks the reader to pay close attention to particular patterns that appear in the drawing process, patterns that he uses to segue the reader into the mathematics that is inherent in the process as well as the drawings.

Gerdes focuses on three areas of mathematics that can be found in the Cokwe drawings. First, he leads us in simple progressive steps to some nice connections between basic number theory and the drawing process. He then encourages us to try to find similar patterns in more complicated drawings. However, in this instance there is little guidance, so it is not immediately clear what to look for or in some cases how to complete the drawings. Moving on, he studies the different symmetries that can be found in Cokwe sand art. He does a nice job introducing the various types of symmetry and helping the reader look for them in the art. He ends, at least mathematically, with an exploration of figurative numbers found within the pictures and sums that can be computed using those numbers. In this case the mathematics is neither inherent in the drawings (as was the symmetry) nor in the process of creating the drawings (as was the basic number theory) but instead it is only in the rectangular lattices of points that act as a framework for the drawings.

The writing strikes a friendly conversational tone, inviting the reader along on a journey rather than giving instruction. This comfortable tone keeps the text free of overly long or precise descriptions. The exercises in the main body of the work all have solutions near the end of the text and there are some additional exercises tacked onto the end of the text without solution.

Gerdes has created an enjoyable work that helps teach that there is math to be found all around us if you are willing to look for it. What is perhaps not sufficiently stressed is the distinction between mathematics that can be found in a work of art and mathematical thinking that is a deliberate or inherent part of the work. In particular, the results concerning figurative numbers, while interesting, are not in any apparent way inherent in the Cokwe sand art, whereas the basic number theory and symmetries seem to be. This work should be accessible to eight to fourteen year olds, though the younger children may need greater guidance.

Chuck Rocca is an associate professor at Western Connecticut State University. His research in the past has been in the field of combinatorial group theory but recently he has been moving toward history of mathematics. In particular he is interested in the history of cryptology and the history of mathematics/science around the seventeenth century. He is also interested in the exploration of the responsible use of technology in the classroom. He can be reached at roccac@wcsu.edu.