Proportions are a mathematical concept that defines the relationship between components or between the parts and the whole of a work, and due to their visual appeal, they are widely used in architecture and visual arts. The primary aim of this research is to examine geometric proportions in Sasanian palaces. This study employs a descriptive-analytical method, using geometric designs such as the golden rectangle and Fibonacci patterns to investigate the application of golden proportions in Sasanian palaces. Findings indicate that in the early Sasanian period, architects employed static and simple dominant geometry, focusing on square modules (1:1), axial symmetry, and Euclidean geometry. However, the architecture of the middle to late Sasanian period became more dynamic and complex. During this era, while maintaining Sasanian principles (symmetry), strong evidence of the use of golden ratios, the number Phi (Φ), golden spirals, and intersecting grid systems in the spatial organization of large-scale structures is observed. The complexity of floor plans increased, and dynamic geometry was used to achieve visual harmony and organize large architectural complexes. Thus, Sasanian architects employed a precise system to control the proportions of length, width, and height of spaces, which not only ensured structural order but also embodied sacred meaning and beauty in the architectural form.
Tarviji et al. (Sat,) studied this question.
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