The hidden geometry

A journey of discovery

My curiosity for ethnomathematics began with the work of Paulus Gerdes, a leading investigator in the field. I was fortunate to participate in a study with Oxford University students on Sipatsi basketry in my home province. It was during this study that I made a profound discovery: the patterns in my own grandmother’s baskets held an ancient, sophisticated knowledge of geometry.

Inspired by this revelation and Gerdes’ work, I became fascinated with the culture and geometry of Southern African women. This provided a deeply meaningful connection to my African roots and sparked the realisation that this knowledge could make mathematics exciting for everyone.

From Ingwedi to Uchwephesha

We celebrate the mathematical genius found in various traditional crafts. This recognition of skill proves that these objects were never “primitive” or “accidental”. They are the results of a rigorous, lifelong pursuit of perfection.

Sipatsi

The Sipatsi, traditional Tonga woven handbags of Inhambane, are perhaps the most sophisticated examples of strip patterns (or frieze patterns) in the world.

While a scientist might see seven possible symmetry groups in a strip pattern, a Tonga weaver sees a story. Using a machete to prepare the fibre and wet sand to sketch her ideas, the weaver creates motifs that repeat endlessly.

Baskets at work: Functional geometry

The shape of a basket is never accidental. It is a direct response to physics. The Zulu beer basket (Isichumo) has a bulbous shape and a tiny opening designed to minimise the surface area of liquid exposed to air, while the tight weave expands when wet to become completely water-tight.

The Tonga diaspora: A shared geometric DNA

As the Tonga people migrated, splitting into groups across Mozambique, South Africa, Zambia and Zimbabwe, our languages changed and our dialects shifted. But our weaving DNA remained. Compare a Sipatsi from Inhambane with a Tonga basket from the Gwembe Valley in Zambia and the same mathematical roots are visible.

See Dathonga Designs

Unlocking hidden patterns

Everywhere you look today, the architecture, the domestic habits, the crafted objects and the daily rituals carry profound purpose and structure. The mathematician G.H. Hardy once famously stated that a mathematician, like a painter or a poet, is a maker of patterns. For centuries, Western academia operated under the assumption that mathematics could only exist within written symbols, formal proofs and rigid equations. However, the women of Southern Africa have been writing mathematics for millennia through the medium of fibre, clay, skin and earth.

These patterns are not merely aesthetic decorations; they are algorithms. When a weaver creates a pattern, she is following a set of logical rules, a mental program, that dictates how many strands must be skipped, where the colour must shift and how the symmetry must be maintained as the vessel or mat grows in three dimensions.

The recursive mind and African fractals

One of the most revolutionary insights into African design came from Ron Eglash, who discovered that many traditional African architectural layouts, textile designs and artistic motifs are based on fractal geometry. While classical European geometry is often Euclidean, relying on simple rigid shapes like circles and squares, African geometry is frequently fractal, grounded in self-similarity, scaling and recursive iteration.

Sona: Tchokwe sand drawing

The sona (singular: lusona) of the Tchokwe people of northeastern Angola, extending into parts of northwestern Zambia and the Democratic Republic of Congo, represent one of Africa’s most sophisticated indigenous geometric traditions. Traditionally drawn in the sand by specialists known as akwa kuta sona (those who know how to draw), these pictograms serve as vital mnemonic devices for passing down history, proverbs, fables, cosmological beliefs and ethical values from one generation to the next.

Sipatsi: The Thonga strip pattern

The Tonga people of Mozambique have developed a unique way of using colour inversion. Because they use a double-thickness weaving technique, the pattern you see on the outside of a Sipatsi is often mathematically mirrored or inverted on the inside.

This requires the weaver to visualise the three-dimensional geometry of the bag before the first strip is even placed. Fieldwork with these women reveals that they do not use rulers; they use the proportions of their own fingers and the mental maps passed down from their grandmothers.

Mats across Southern Africa

Throughout Southern Africa, mats serve as canvases for high-level mathematical exploration, using complex interlacing techniques.

Titja: The coil geometric pattern

Coiled weaving is practised by women from southern Africa, from Angola to Mozambique: the Tsonga, Swati, Zulu, Subiya and Mbukushu peoples, among others, who hand-spin sisal thread (umtiye) around a rigid grass coil to create vessels known as a sitja (plural: titja). Because the coil is not a perfect geometric circle, weavers intuitively solve complex spatial problems to guarantee approximate rotational symmetry, manage stitch counts and measure distances seamlessly across circuits.

Tinlhèlò / Gitandri: Structural geometric pattern

The Tinlhèlò technique (also known as Gitandri) is a traditional African hand-weaving practice rooted in indigenous utility, architectural craft and complex geometric design. Historically passed down through generations across Mozambique, most notably among the Bitonga-speaking communities of the Inhambane region, this method uses raw, locally harvested materials such as Ilala palm fronds to build items that require exceptional structural integrity and geometric precision.

Beadwork: A woman’s craft

Beadwork is a powerful women’s craft across Southern Africa, demonstrating a sophisticated vocabulary of symmetry and proportion. From the ovilame ornaments of Ovimbundu women in Angola to the intricate geometric regalia of the Ndebele, Xhosa and Zulu, every bead placement reflects rigorous structural planning.

Oku-taleka: Decorated pottery

Pottery has traditionally been a women’s art form across many societies. The Nyaneka-Humbe women in Angola decorate their ceramics with geometric drawings called oku-taleka (“to be looked at”). These designs feature rotational symmetry with motifs repeated an exact integer number of times around the neck of the pot, requiring potters to intuitively calculate spacing and proportions before executing the design.

Litema and Ikghuptu: The algebra of the wall

Southern African women create wall decorations known as Litema. These are not just paintings; they are modular systems built from a single unit cell, usually a square.

Nembo: Geometry etched on the body

The vanishing tradition of Nembo (tattoos) among the Makonde, Yao, Tsonga and Ndau people showcases a deep knowledge of axial symmetry.

Machiras: The woven textures of Mozambican tradition

Beyond basketry, pottery and murals, textiles represent a vital canvas where Mozambican artisans weave culture, identity and geometry. Among the historical and traditional textile traditions of Mozambique, machiras (traditional hand-woven cloths produced in regions such as Zambézia and northern Mozambique) stand out as powerful examples of indigenous applied mathematics and craft.

The botanical mental map of the African landscape

Master weavers navigate a precise botanical mental map across Southern Africa’s 24,500 plant species.

Form, function and the future

In Africa, where art is often a daily activity, the form of a piece is profoundly influenced by its function, resulting in a timeless, minimalist aesthetic. Basketry, perhaps more than any other craft, represents the finest blend of African culture, technology and environment. Yet the deep connections between these elements are often poorly understood outside of the communities that create them.

While the debate over whether an item is art or craft is long-standing, it is indisputable that function shapes form, and that high-quality craftsmanship has always been a recognised value.