From complexity of architecture to geometrical rule. The case study of the dome of San Carlino alle Quattro Fontane in Rome.

"This study, started by a collaboration of representation and mathematic researchers, intends to verify the correspondence between the geometrical and the built shape of the dome of San Carlino in Rome, designed by Francesco Borromini. The transition from a geometrical model to its construction, in fact, is also influenced by factors related to the building yard practice, which can also lead to significant changes over the initial idea. For this reason a new survey has been conducted, which analyzed the vault in detail, especially in the sequence of panels which characterize the soffit. The comparison between the model derived from instrumental survey and a mathematical-analytic model, based on parametric curves and arithmetic progressions, has allowed us to understand the transition from geometrical form, measured on the impost of the vault, and his space development; at the same time, the comparison between design drawings and the survey model has allowed us to formulate some new hypotheses about the relationship between Borromini’s design and constructive method. "