The term morphogenesis in architecture is usually associated with parametric design strategies. I intend ‘morphogenetic’ in a different sense. Architecture in general, and architectural education in particular, are awash in proposals that might be best described as ‘biomorphic.’ Yet, in my experience, students and practitioners have neither fundamental understanding of shape-as-surface nor the vocabulary necessary to describe such designs. This vocabulary, including a powerful generalisation of biomorphic shape, is readily available in the work of Carl Friedrich Gauss (1777–1855). Gauss’s generalisation recognised that there are only three types of surface: positively curved, negatively curved and surfaces of zero curvature. This paper offers a concise exposition of Gauss’s formulation, a proposal for a vocabulary sufficient to clearly discuss such shapes in design contexts and a plea for an architectural pedagogy that moves beyond notions of space as bounded emptiness (i.e. beyond perspectival constructions). These reflections are a product of an educational experiment conducted in a first year architectural studio during the spring of 2017. Surform is a neologism, shorthand for ‘shape conceived as surface.’
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