Elliptic Paraboloids in Circumpolar Vernacular Architecture

Nancy Mackin
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 621–624


This workshop employs mathematics to explore characteristics of elliptic paraboloid forms common to tradition based country buildings from distinct regions of the circumpolar north. To begin, short videos show full-scale reconstructions of three dwelling types from Indigenous peoples’ tradition: Sápmi goahti (birch-framed turf-clad dwellings from northern Scandinavia), Inuvialuit qaluurvik (willow-framed skin-and-moss clad dwellings from the western Canadian Arctic), and Inuinnait iglu (snow block dwellings from the high Arctic of North America). Workshop participants then build scale models of the three types. Participants’ models, combined with dimensional information about the full-scale reconstructions, facilitate mathematical analysis of the vernacular structures. Conical frusta and second-order polynomials integrated in applicable dimensions describe the shapes and calculate their interior volumes. Efficiencies are calculated and compared both qualitatively and quantitatively: mass of materials required to build each vernacular structure, energy expended during construction, and potential for passive heating in the basic form and detailed design. Discussions will address bio-mathematics, including the natural strengths of certain forms, whether made of bent wood or stacked snow blocks; ecological advantages of the housing types; on-going usefulness of reconstructed vernacular architecture as places for teaching and survival shelters; comparisons with “formal” architecture, including Antoni Gaudi; and the value of long-resident peoples’ architectural knowledge.