Geometric Modelling of Traditional Architectural Patterns in Hausa-Fulani Settlements in Sokoto State

This study examines the geometric principles embedded in the architectural patterns of traditional Hausa-Fulani settlements in Sokoto State, North West Nigeria, situating vernacular building forms within a rigorous mathematical framework of symmetry, tessellation, and fractal geometry. Traditional Hausa architecture, known for its distinctive earthen construction and ornamental facades, has received considerable attention from anthropologists and architectural historians, yet its mathematical foundations have not been systematically analysed in the contemporary literature. The study documents architectural patterns from forty compounds in the Sokoto metropolis and the ancient town of Gwandu through photographic survey and geometric measurement, cataloguing recurring motifs and structural forms. Symmetry group analysis is applied to classify wall decorations and courtyard layouts according to their plane symmetry groups, while box-counting methods are used to estimate fractal dimensions of selected facade patterns. Results indicate that Hausa-Fulani architectural ornamentation exhibits high mathematical complexity, with fractal dimensions consistent with natural and deliberately designed aesthetically pleasing patterns observed across multiple cultural traditions. The study contributes to the emerging interdisciplinary field of ethnomathematics in Nigeria and argues for the incorporation of indigenous geometric knowledge into secondary and tertiary mathematics curricula. It also provides a documented record of mathematical heritage at risk of erosion through modernisation. Keywords: geometric modelling, Hausa-Fulani architecture, tessellation, fractal geometry, ethnomathematics