To expand search, see Sub-Saharan Africa. Laterally related topics: TheTshokwe, The Mursi of Ethiopia, The Bambara of Sudan, South Africa, The Bushmen (southern Africa), Ghana, The Bakuba of Zaire, BeninCity, Nigeria, Cameroon, Ethiopia, Mali, Mozambique, and The Kpelle of Guinea.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Ascher, Marcia. Graphs in cultures. II. A study in ethnomathematics. Arch. Hist. Exact Sci. 39 (1988), no. 1, 75--95. (Reviewer: M. P. Closs.) SC: 01A10, MR: 90d:01003.
Discusses the cultural background and mathematical properties of the continuous graphs traced by the Booshong and Tshokwe, who live in the Angola/Zaire/Zambia region of Africa. The Bushoong are a subgroup in the Kuba chiefdom, and exchange their art for food and raw materials. They have interesting ways of classifying designs, which are touched on by the author. The problems in continuous tracing among the Bushoong are primarily the domain of children. Ascher discusses the tracing algorithms used. In the Tshokwe, continuously traced graphs play an important role in the story-telling tradition. The author gives examples of how some diagrams are used to discuss a rite of passage and in connection with the muyombo trees representing the village ancestors. In some cases, the notion of inside/outside is important (an aspect of the Jordan curve theorem). Ascher discusses geometric characteristics of the graphs (for example, many are regular of degree 4), and algorithms for drawing the curves. Closely related topics: Continuous Tracing Problems, TheTshokwe, and Storytelling Traditions.
Katz, Victor J. Essay reviews of Ethnomathematics [Brooks/Cole, Pacific Grove, CA, 1991; MR: 92c:01006] by M. Ascher and The crest of the peacock [Tauris, London, 1991; MR: 92g:01004] by G. G. Joseph. Historia Math. 19 (1992), no. 3, 310--315. SC: 01A07 (00A30), MR: 1 177 496.
Katz reviews and contrasts Marcia Ascher's book Ethnomathematics: A Multicultural View of Mathematical Ideas and George Gheverghese Joseph's book The Crest of the Peacock: Non-European Roots of Mathematics. He finds that both correct serious omissions in the literature (and in particular, in Morris Kline's Mathematical Thought from Ancient to Modern Times). Joseph focuses on the history of mathematics in the large civilizations of ancient Egypt, Babylonia, China, India, and the Islamic World. He wanted to highlight "(1) the global nature of mathematical pursuits of one kind or another; (2) the possibility of independent mathematical development within each cultural tradition; and (3) the crucial importance of diverse transmissions of mathematics across cultures, culminating in the creation of the unified discipline of modern mathematics." Katz seems disappointed only in the third thesis, "because the documentary evidence for transmission of mathematical ideas is lacking." (For example, he notes that "whether Diophantus was directly influenced by the Babylonian tradition is a subject of scholarly debate." Joseph's treatment of Indian mathematics seems to be particularly good "especially since it is difficult to find this material in other sources." The focus of Ascher's book is completely different. She looks at traditional non-literate peoples. As Katz notes, "She has no intention of claiming that the mathematics developed in the cultures she discusses had any influence on developments elsewhere. Her main goal is simply to show that mathematical ideas, even if not developed by those called mathematicians, can be found in many societies if one only knows where to look." Katz reports examples as coming from the Inuit, Navajo, Iroquois, and Incas of the Americas, the Malekula, Warlpiri, Maori and Caroline Islanders of Oceania, and the Tshokwe, Bushoong, and Kpelle of Africa. This very useful review concludes by highly recommending both books. Closely related topics: Ancient Egypt, Sumerians and Babylonians, China, India, The Islamic World, The Inuit, The Navajo, The Iroquois, The Inca, The Malekula of Vanuatu, The Warlpiri, The Maori, The Caroline Islands, TheTshokwe, and The Kpelle of Guinea.