Cloister vaults between synthetic, analytic and built geometry: il vólto antonelliano in Torino

Our contribution is part of a research project aimed at investigating Geometry as a cultural substrate and shared language between Architecture and Mathematics. In this sense, spatial visualization plays a crucial role in architects’ educations and heavily draws on making use of mathematical instruments. In this intention the ‘nudo e schietto’ (naked and explicit) architectural model, as theorized by Leon Battista Alberti, turns out to be the most effective one: it favors the objectivity of the geometric description, having less details, even if final results are not necessarily rigorous. Analogously, from a mathematical point of view, the model is a description of a reality through its formalization in equations, while the physical model that materializes it is a mediation between descriptive rigor and practical feasibility and therefore forgets part of the generative geometric consistency while remaining adequate to purposes for which it was produced.