 # Art as visual mathematics

on Friday, 28 February 2014. Posted in maths, science & technology

a2+ b2= c2.. This equation is known as the Pythagora’s Theorem. It relates to right-angle triangles, where the square of the hypotenuse (c) is equal to the sum of the squares of the two other sides. While a perception has been created that mathematics is far removed from African norms, several forms of art and design prove differently.

A study of indigenous mathematical knowledge found that inhabitants of the Basotho Cultural Village used a variety of mathematical concepts extensively. In particular, the design and manufacturing of traditional grass artefacts, such as the traditional baskets, traditional hats, and other items such as Motlhotlho (strainer), employed mathematical techniques. The research revealed that even with an average level of formal education of Grade 4, the inhabitants of the village were familiar with mathematical concepts such as estimation, patterns, geometry, and symmetry. Mathematical concepts are widely used, however, the terminology and understanding is not as expressed in ‘western’ mathematical literature. A cursory overview of artefacts, design and art works across Africa will reveal the wide use of geometrical ideas in wood work, ivory pieces, pottery, paintings, weavings, mats and baskets. This again demonstrates that mathematical concepts are embedded and interwoven into the ‘traditional’ daily activities of various African cultures.

Another art form well recognised for its mathematical use is traditional Ndebele art. In her work, world-renown Ndebele artist Esther Mahlangu uses complex patterns of angles and lines, symmetry and proportions, which are also mathematical formulas found in geometry and trigonometry. While recognised as exquisite art, the Ndebele paintings are also useful for teaching mathematical concepts that can assist learners to understand squares, rectangles, angles, as well as in measuring, and understanding and solving problems like volume.

In Angola it is the design and art tradition of the Tchokwe, also known as ‘sona’ drawings, that reveals mathematical reasoning in their cultural practices. The traditional drawings of the Tchokwe are represented as standardised pictograms. The mathematical properties of the pictograms can be used as tools for arithmetical problems such as the ‘find the missing numbers’ or ‘find the missing figures’. Other pictograms can be used in units of measurements of squares and rectangles. Sona drawings illustrate the interactions between mathematics and patterns, and employ mathematical concepts such as common divisors, the Euclidean algorithm for common divisors, and the implementation of many types of symmetry groups.

The use of mathematical concepts across various African cultural practices demonstrates that mathematics is by no means foreign to Africans. Where South Africa’s bantu education was premised on the notion that Africans were incapable of doing mathematics, historical evidence proves quite the opposite. The examples cited above show a different approach to mathematics. Within this different approach, it shows that at a conceptual level, even those without formal education are highly capable of understanding mathematical concepts and applying them in the context of ‘modern’ mathematics. In other words, the mathematical concepts used to design and manufacture certain artefacts, are also used in purchasing goods and navigating the present day economic environment.

Mathematics is a universal activity. All peoples across the world developed mechanisms and systems for counting, locating, measuring, designing, playing and explaining. However, different ethnic groups arrived at their own uses and implementation of mathematics in their daily activities. In that sense, the development of mathematics has not been a unilinear process. The development has depended on the economic, social and cultural conditions of particular cultural groups. It was by and large the standardisation of mathematics out of which ‘academic mathematics’ emerged. Other classifications of mathematics have been developed by researchers and can be categorised as:

• Indigenous mathematics: creative mathematical education that uses indigenous mathematics as a basis for further mathematical development.
• Socio-mathematics: the applications of mathematics in the lives of African people, and conversely, the influence of African institutions upon the evolution of their mathematics.
• Informal mathematics: mathematics that is transmitted and learnt outside of the formal system of education.
• Socio-cultural mathematics: mathematics of African games and craft work that belongs to a socio-cultural environment.
• Spontaneous mathematics: mathematics that is developed spontaneously.
• Oral mathematics: mathematical knowledge that is transmitted orally from one generation to the next.
• Oppressed mathematics: mathematical elements in the daily life of certain population groups but that is not recognised as mathematics by the dominant ideology.
• Non-standard mathematics: mathematical forms such as street mathematics developed outside of ‘academic’ or ‘school’ settings.
• Hidden or frozen mathematics: mathematical knowledge that has been lost, for example through colonisation, that may need to be reconstructed or ‘unfrozen’ through old techniques such as basket making.

For a country like South Africa, where the standard of mathematics is said to be among the lowest in the world, understanding the socio-cultural context of mathematics may be constructive in strengthening maths education. There are existing forms of indigenous knowledge that can be used to do so. It will take political will to ensure that it is implemented for the betterment of the nation’s future.

Mogege Mosimege, Indigenous Mathematical Knowledge at South African Cultural Villages: Opportunities for Integration in Mathematics Classrooms