A Theoretical and Practical Analysis of Geometry and Proportions in Discontinuous Double-Layer Architectural Systems

Abstract : Despite the stylistic and structural significance of discontinuous double-shell domes in architectural heritage, limited scholarly attention has been devoted to their geometric foundations. This case-based study investigates the relationship between theoretical and practical geometry in the design and construction of discontinuous double-shell domes. The research seeks to answer two main questions: (1) What is the connection between theoretical and applied geometry in the shaping of such domes? (2) What are the key factors influencing their design and construction process? The study begins with a review of the theoretical foundations of geometry in architecture, followed by an analysis of a selected case study to trace the application of geometric and proportional principles derived from the theoretical phase. Through this analysis, the underlying geometric logic of the dome’s formation is decoded. The results reveal that the dome was designed based on a premeditated geometric system involving fundamental shapes—square, circle, and pentagon—with proportions governed by the golden ratio. These proportions are consistently manifested in the plan, section, and elevation. The study contributes to the understanding of traditional geometric practices and their potential application in the conservation of historical domed structures as well as the design of contemporary shell architecture.