A Puzzling Set of Stucco Coffers from Portici: Archaeology and Mathematics Working Together

Abstract

Archaeology and mathematics work together to reconstruct the form and dimensions of a vault originally adorned with a set of twenty-five stucco coffers in the shape of concave octagons, today conserved in the Archaeological Museum in Naples. Measurements were taken to determine the curvature and orientation of the coffers. Two methods used to establish the size of the vault permitted an approximation of the vault width, making it possible to propose limited possibilities for the number of coffers transversally to the vault, and how they were displayed on it. Further studies were made of the decorative scheme in order to suggest a plausible construction process for the coffers with tools and techniques usual at the time, using only arcs of circles. For this, the front side of the coffers was considered to be plane, which led us to establish that they were included in an all-over scheme of squares and that the concentric octagonal frames were very likely drawn from two families of circles. Then differential calculus showed us that the differences due to the plane approximation of the cylindrical shape of the vault were negligible with regard to the precision of the guidelines drawn in situ. Finally we suggest a complete decorative scheme, using various clues such as subject, orientation, curvature and colours of the tesserae decorating the framing.