Muqarnas: The Intertwined Story of Architecture, Mathematics and Geometry

Abstract The research investigates the origins, morphology, and geometric principles of muqarnas by examining Sicilian sacred architecture produced between the Arab domination and the reign of Frederick II. These buildings, shaped by Islamic, Byzantine, and Norman influences, preserve early examples of muqarnas used to mediate between vertical and horizontal surfaces. The study contextualizes these architectures within broader Mediterranean and Middle Eastern traditions, retracing the formal genesis of muqarnas and their symbolic meanings. A central component is the reexamination of practical geometry manuals produced between the ninth and thirteenth centuries, particularly the works of al-Būzjānī and al-Kashi, which reveal empirical and mathematical methods for constructing muqarnas units. Instrumental surveys, photogrammetry, and 3D modelling are applied to Sicilian case studies and compared with examples from Turkey and Uzbekistan to identify shared geometric matrices and verify tracing hypotheses. The results contribute to defining a protocol for analysing muqarnas morphology.