Read This! The MAA Online book review column Women, Art And Geometry In Southern Africa by Paulus Gerdes Reviewed by Walter S. Sizer

A major thrust of Women, Art and Geometry in Southern Africa is the description and illustration of some of the many designs which appear in southern African women's crafts. Over 180 designs are actually pictured in the book. These patterns come from many different sources, many from items in the author's private collection. Included are decorations from woven handbags, baskets, mats, tattoos, beadwork, murals, decorated pottery, and string figures, to list some of the diverse sources of the designs.

The author connects these designs to mathematics by considering the symmetries they display. Some of the work can be thought of as giving part of infinite strips and can be analysed in terms of the various symmetries of such strips. This is done in detail in the case of designs on woven handbags from Inhambane, a province of Mozambique. For some of the possible strip symmetry groups a description of the symmetries is given and an example of a woven design having that symmetry group is pictured. It turns out that all seven possible strip symmetry groups are represented in the woven handbag designs from this area. Decorations on woven grass brooms from Lesotho, on pottery from diverse regions, and on beaded ornaments are also treated in part as strip designs and discussed in terms of strip symmetries.

Other patterns are treated as finite designs and analysed in terms of global symmetry. Many are examined and seen to have dihedral symmetry groups, generated by a rotation of finite order and a reflection, and some are seen to have cyclic symmetry groups, generated by a rotation of finite order. Other examples showing bilateral symmetry are given. Some of the patterns considered in this way include tattoos (various Mozambiquan tribes), string figures made by Thonga girls (Mozambique and South Africa), woven mats from South Africa, and pottery decoration from Angola. A concern of the author which comes through often in this book is the potential use of native designs in the teaching of mathematics. As Gerdes is an educator involved in teacher training in Mozambique he writes from direct experience.

He uses some of these designs in the classroom with students for whom the designs are part of their own cultural background. However, the designs might also work well to introduce other students to some of these same mathematical concepts. One chapter (11) of Women, Art and Geometry in particular focuses on the use of patterns to get students to discover and justify relationships. At numerous other points in the text Gerdes asks questions which focus on the relationship between crafts and mathematics, and he reflects further on this connection in a short epilogue. An appendix contains a report by a former student, Salimo Saide, on pottery decoration, showing a link between the mathematics he was studying and the traditional designs he had seen at home.

In the epilogue Gerdes gives several references both on the interplay between mathematics and culture and on symmetry. In addition, his lengthy list of references also includes several pieces dealing with anthropology and history, the arts, African education, and mathematics education.

I found Women, Art and Geometry in Southern Africa interesting and enjoyable reading. The fact that the mathematics is relatively easy does not destroy that interest. I especially appreciated the great number of designs actually shown in the book--expecting in such a work much more verbiage on many fewer patterns--and the additional references given in case I wanted to pursue various topics further.

A primary audience for this book, of course, is those who will be teaching mathematics in southern Africa. I would expect, however, that others interested in incorporating native traditions into the study of mathematics would find many of the ideas presented in this book would carry over from one culture to another. As Gerdes says of his own situation teaching in Mozambique (p. 199), "...the African cultural heritage should be the starting point in the development of the mathematics curriculum in order to improve its quality, to augment the cultural and social self-confidence of all pupils, both girls and boys." Omitting the first two words of the quotation, one gets a statement that applies to others teaching students from other distinctive cultural heritages.

Publication Data: Women, Art And Geometry In Southern Africa, by Paulus Gerdes. Africa World Press, 1998. Paperback, 244 pages, $21.95. ISBN 0-86543-601-0 (hardcover), 0-86543-602-9 (paperback).

Publisher's Address: Africa World Press, P.O. Box 1892, Trenton, NJ 08607 (or P.O. Box 48, Asmara, Eritrea).

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Walter S. Sizer is a professor of mathematics at Moorhead State University in Minnesota. His other interests include reading, travel, and nature, especially bird watching.

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