METROLOGICAL PHOTOGRAMMETRY AND STOCHASTIC ANALYSIS OF THE PANTHEON'S ROTUNDA: VERIFICATION OF A PROPORTIONAL CANON

Abstract

The Roman Pantheon represents the most significant and exceptionally preserved monument of classical antiquity. Despite extensive archaeological and geodetic surveys, the internal proportional system of the Rotunda's geometry remains an open question in classical metrology. Standard attempts to reconstruct the design grid using the official Roman foot (pes monetalis ≈ 0.296 m) consistently yield non-harmonic, fractional values and notable residuals. This study applies a multivariate and stochastic metrological analysis based on a linear standard of 0.623538 m (Holy Cubit – SL / Sacred Cubit – SC) to the internal structural elements of the Rotunda, leveraging contemporary high-precision geodetic measurements and 3D laser scanning data. The results demonstrate that all key dimensions of the Rotunda correspond to whole modular integers with a mean absolute residual of only 1.6 mm (relative error < 0.03%), proving over 45 times more precise than any other Mediterranean standard. A Monte Carlo simulation () confirms that the probability of this modularity occurring by chance is .