Measurement-Based Geometric and Aesthetic Analysis of the Ellipsoidal Roofing System of Kutlubey Mosque in Isparta

The geometric configuration of curved roofing elements in historic structures provides valuable evidence of the design knowledge and construction practices of their respective periods. This study examines the geometric and proportional organization of the elliptical roofing units symmetrically positioned along the four cardinal directions around the central dome of the prayer hall roofing system of Kutlubey Mosque in Isparta. Comprising a central dome, four elliptical roofing units, and corner domes, the mosque’s roofing system represents a distinctive geometric composition within Anatolian mosque architecture. The research integrates in situ manual and laser-based measurements with mathematical modeling methods. The major and minor semi-axes of each elliptical roofing unit were determined, and their geometric characteristics were evaluated using the axial ratio and eccentricity. The resulting ratios were compared with the traditional ratio of 1.5 and the golden ratio of 1.618. The findings indicate that the eastern and western roofing units exhibit consistent geometric characteristics despite their differences in scale and show a notable proportional proximity to the golden ratio. By contrast, the northern and southern units deviate more substantially from these reference ratios, suggesting that the four elliptical roofing units were not generated according to a single, invariant proportional rule. Nevertheless, the symmetrical arrangement and directional differentiation of the units demonstrate that the roofing system was organized according to a deliberate geometric hierarchy rather than through an arbitrary combination of curved forms. The results provide quantitative and reproducible evidence for interpreting the design geometry of Kutlubey Mosque and contribute to the geometric documentation of historic roofing systems. This study establishes a methodological framework for interdisciplinary research encompassing architectural history, design geometry, and the geometric documentation of historical buildings.