Mathematics in West Africa

Summary: Mathematics has long been used in west African art, architecture, industry, and music.

The peoples of west Africa have a long history of using mathematics. Everyday uses were similar to mathematics in other traditional societies around the world. Farmers measured their fields and counted their crops, anticipating the production figures. Fishers designed boats to carry them off the coast and prepared nets for catching fish. For both, there were processes to handle their products, either for immediate consumption or—with additional mathematics—for sale in local or distant markets. Markets served as centers of trade and also as centers of mathematical calculations of quantities and sizes, profits and losses. Everyone designed and built houses, often round in shape, which calculus shows to provide the maximum area for a given perimeter. As larger societies and governing units grew beyond the villages, mathematics played a role in governments, from taxation and salaries to the design of palaces and warehouses.

Mathematics in West African Art

West Africa has long been known for its art, textiles, music, and dance. Mathematics is central to the creative and performing arts. Some particular west African examples include carved sculptures, wall paintings, tie-dyed textiles, and woven cloth. Sculptures often show symmetries, not only of human features but also of geometrical designs and proportions of animals, village scenes and daily life, and abstractions of circles, rhombi, stars, and repeating patterns. Often, the palaces of chiefs or emirs became sites of art, especially with designs on the walls or in the architecture of the structure—all incorporating geometrical designs.

Throughout west Africa, textiles have been a central part of culture. From the multicolored patterns in Sierra Leone to the deep blues and indigos of the Hausas, the techniques of dyeing cloth have been popular, especially with tied or sewn folds of the cloth to yield intricate patterns of dyed and nondyed areas of the material. Often, the use of symmetries and Euclidean geometric constructions is necessary to produce the desired circular, radial, rhombic, and zigzag patterns. Woven cloth includes the brightly colored kente of Ghana, the metallic shine of the Okenne cloth of western Nigeria, and others. Weaving requires engineering mathematics to design and build looms, and then careful planning so that the strips of material that come off the looms will fit together in two-dimensional symmetrical arrangements.

These traditional artistic products have been carried into the present day. Traditional designs are now seen in modern buildings throughout the region. Fashionable textiles sometimes use new materials or printed cloth but continue the geometric traditions. Kente has become a popular material not only in Ghana but also in the United States, especially the symmetrical strips used as wraps and ties. Recent studies by ethnomathematician Ron Eglash have demonstrated a variety of uses of fractal patterns in traditional west African arts, ranging from repeating smaller patterns in the geographical arrangement of savannah villages, to necklaces and bracelets, carvings from Mali of increasingly small antelopes, and even corn-row hair braids that repeat smaller shapes as the pattern goes from the forehead and temples to the rear of the head.

Music and dance from west Africa are famous to both ethnomusicologists and jazz aficionados—and to ethnomathematicians. The rhythm patterns, especially from complex drumming structures, often involve unusual time signatures and alternations of loud and soft sounds. The three-dimensional movements of dance, like the carvings and textiles, show complex symmetries and geometrical arrangements of the dancers.

Early in the second millennium, Islam was introduced in west Africa, along with Islamic mathematical studies. This introduction added to the original practical base of west African mathematics, as west Africans adapted Islamic counting methods, reflected not only in the languages of west Africa but also in theoretical mathematics studied at scholarly centers such as Timbuktu (in modern Mali) and Katsina (in modern Nigeria).

Mathematics and West African Development

Since gaining independence, mostly in the 1960s, west African countries have moved rapidly to modernize. In the process, they have shown a dynamic use of mathematics—on a smaller scale than but similar to the technical mathematics of the developed world. Oil production in Nigeria, gold mining in Ghana, and diamond mining in Sierra Leone all use modern mathematical techniques, including those employed by geological surveys, sophisticated industrial equipment design, accounting, marketing, and business management. New businesses are being established to work with cell phones, the Internet, automatic teller machines, television and film production, and other industries that rely on technical mathematics and engineering. Modern freeways connect the larger cities and are designed by civil engineers and urban planners.

Education and West African Mathematics

Education throughout west Africa has grown dramatically since independence—universal primary education remains elusive, but the percentage of children attending school is approaching that goal in several countries. Political independence also brought educational independence, including national curricula offered by the Ministries of Education, the West African Examinations Council’s system of standardized examinations, and locally produced textbooks and teaching materials, using familiar names, places, and situations in examples. Local researchers are studying their own cultures, seeking examples of ethnomathematics in traditional life, often with the goal of using these findings to strengthen the content of school mathematics curricula. With only a few universities in existence at the time of independence, west African countries now have numerous universities. These are often managed by the national governments—though some states of Nigeria operate their own universities and research centers, and the number of private universities is growing. These universities offer degree programs in mathematics, the sciences, engineering, and computer science, all with curricula based on the accepted world standards of these fields. Most countries have professional and scholarly organizations of mathematicians and mathematics educators, and periodically there are regional and continent-wide conferences, such as the meetings of the African Mathematical Union (AMU). The AMU’s activities include the Commissions on Mathematics Education in Africa, Women in Mathematics in Africa, the African Mathematics Olympiads, and publishing the journal Afrika Matematica. Thus, even as west Africa maintains its traditional uses of mathematics in the arts and music, it has also become a part of the modern world mathematics community.

Bibliography

Eglash, Ron. African Fractals: Modern Computing and Indigenous Design. New Brunswick, NJ: Rutgers University Press, 1999.

LaGamma, Alisa, and Christine Giuntini. The Essential Art of African Textiles: Design Without End. New York: Metropolitan Museum of Art, 2008.

Mendonsa, Eugene L. West Africa: An Introduction to Its History, Civilization and Contemporary Situation. Durham, NC: Carolina Academic Press, 2002.

Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Culture. 3rd ed. Chicago: Lawrence Hill Books, 1999.