AI Insight
This study analyzes the geometric patterns of coffered domes in the Roman Pantheon and Hawksmoor's ceiling at All Souls College, Oxford, proposing that their grid-like designs follow conformal mapping principles similar to Mercator's projection. The researchers demonstrate mathematically that the ribs form orthogonal intersections that can be understood as angle-preserving transformations of a flat rectangular grid onto curved surfaces, minimizing elastic and gravitational energy. Their model successfully predicts the size and location of individual coffers without adjustable parameters, matching both photographic evidence and direct measurements of the Pantheon.
Why it matters
This work reveals potential mathematical principles that could have guided ancient and early modern architects in creating structurally stable coffered domes, suggesting that practical construction methods naturally converge on optimal geometric solutions. The findings could inform modern architectural design and restoration efforts for historic structures with complex curved surfaces.
Understand the Science
⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
-cross
Abstract: The dome of the Roman Pantheon is coffered with ribs surrounding sunken lacunaria, thus forming a grid. How this is achieved given the curvature of the dome has long been a subject for study and speculation. Although detailed measurements now exist, thus far no single principle has emerged which fixes the overall geometry. Similar coffering occurs in Hawksmoor’s design for the ceiling of the Buttery in All Souls College, Oxford. Both these examples are doubly curved, making their tiling with (almost) square coffers problematic. We address this using methods of differential geometry. Observing that the ribs intersect orthogonally, we hypothesize that they are images under a conformal (angle preserving) mapping of a uniform M x N tiling of a planar rectangle with squares. This is unique and is the inverse of Mercator’s projection of the ceiling to the rectangle. It minimizes an energy functional which captures the sum of the elastic and gravitational energies in the long wavelength limit. Thus, any construction method which is stable to long wavelength deformations necessarily leads to a conformal coffering. This then gives quantitative predictions with no adjustable parameters for the relative sizes and locations of each coffer, which are in good agreement with photographic data, and consistent with direct measurements of the Pantheon. We suggest protocols by which Hawksmoor’s ceiling and the Pantheon might have been constructed without advanced mathematics.
Source: Hawksmoor's Ceiling, Mercator's Projection and the Roman Pantheon