Geometry From Africa

This book draws on geometric ideas from cultural activities from Subsaharan Africa to develop mathematical reasoning.

This book draws on geometric ideas from cultural activities from Sub-Saharan Africa and demonstrates how they may be explored to develop mathematical reasoning from school level through to university standard. Paulus Gerdes provides a thoroughly illustrated and researched exploration of mathematical ideas, motifs and patterns. Many important mathematical points are brought to the fore, not via the formal ``theorem-proof'' method, but in a more schematic and diagrammatic manner. African artifacts, oral traditions, sand drawing and other forms of artwork with a geometric basis, all provide mathematical ideas for discussion in this unique book. Mathematicians and teachers of mathematics at all levels will be fascinated, as will anybody with an interest in African cultures.

The main objective of the book is to call attention to some mathematical ideas incorporated in the patterns invented by women in Southern Africa. An appreciation of these mathematical traditions may lead to their preservation, revival and development. Use of female art traditional forms has implications in the field of mathematics education.

Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

New edition of award winning book "Women and Geometry in Southern Africa: Suggestions for Further Research", published by the "Universidade Pedagógica" (Mozambique) in 1995. The original book contains chapters on geometrical ideas embedded in basket weaving, bead work, wall decoration, tattooing, and ceramics. The expanded edition includes a foreword by Sibusiso Moyo (Secretary of the African Mathematical Union Commission on Women in Mathematics in Africa, and Research Director of the Durban University of Technology, South Africa), afterwords by Ubiratan D'Ambrosio (Brazil) and Jens Hoyrup (Denmark), and the papers "Makwe colour inversion, symmetry and patterns" (Northeastern Mozambique) and "Symmetries on mats woven by Yombe women from the area along the Lower Congo." The book contains also a chapter written by Salimo Saide on the geometry of pottery decoration among Yao women (Nyassa Province, Mozambique). (2013, 276 pp.)

"This volume provides readers with a glimpse into Paulus Gerdes's seminal work on the mathematics of an African tradition - 'sona' geometry, a drawing and narrative tradition from Angola with embedded mathematical ideas. The work represented in this book contributes significantly to efforts by other African mathematicians and mathematics educators to recuperate and valorize mathematical ideas and reasoning that reside in African material culture and cultural practices [...]. Moreover, Gerdes is a prolific contributor of work that reinforces a growing literature available in English of a dynamic research program in ethnomathematics. Uncoveirng the mathematical ideas embedded in a Cokwe cultural practice and providing access to the richness of these ideas are part of the concerns of ethnomathematics. As an ethnomathematician, Gerdes is not a neutral researcher but rather a public intellectual committed to finding ways not only to understand the mathematics of the Cokwe 'sona' tradition but also to raise important questions such as [...] when he observes that the profoundness of the mathematical ideas expressed in the 'sona' 'had started to build up.' With this, his reader is then prompted to ask questions: What happened to the building up of the 'sona' tradition and its mathematical ideas? Why was this development arrested? Answering these questions along with enjoying the beautiful presentation of the mathematics of the 'sona' tradition are the gifts that readers will receive from this wonderful volume"--Arthur B. Powell, p. [4] of cover.

This volume constitutes an updated version of the bibliography published in 2004 by the African Mathematical Union. The African Studies Association attributed the original edition a 'ÂÂspecial mention'ÂÂ in the 2006 Conover-Porter Award competition. The book contains over 1600 bibliographic entries. The appendices contain additional bibliographic information on (1) mathematicians of the Diaspora, (2) publications by Africans on the history of mathematics outside Africa, (3) time-reckoning and astronomy in African history and cultures, (4) string figures in Africa, (5) examples of books published by African mathematicians, (6) board games in Africa, (7) research inspired by geometric aspects of the 'ÂÂsona'ÂÂ tradition. The book concludes with several indices (subject, country, region, author, ethnographic and linguistic, journal, mathematicians). Professor Jan Persens of the University of the Western Cape (South Africa) and president of the African Mathematical Union (2000-2004) wrote the preface.