Introduction: Illustrated lithographic editions of the Shahnameh are important sources for studying the relationship between text, image, and page design in Iranian visual culture. Beyond their historical and artistic significance, these editions offer opportunities to examine the geometric organization of the page and the compositional structure of their illustrations. Proportional relationships among the paper format, text area, image frame, and pictorial elements contribute to the overall visual organization of a page. Analyzing these relationships can reveal geometric patterns, numerical ratios, and methods of spatial arrangement. Comparing illustrations with the same narrative subject across different editions also makes it possible to identify variations in their compositional structures and investigate the extent to which their proportions correspond to established geometric systems, including the golden ratio.
Purposes & Questions: This study aimed to identify and compare the proportional systems observable in three illustrations depicting Zahhak from three Qajar-era lithographic editions of the Shahnameh: the Bombay edition of 1266 AH, the Tabriz edition of 1275 AH, and the Tehran edition of 1322 AH. By focusing on a shared narrative subject, the study examined how proportional relationships were organized at different levels of the page and how these relationships varied across the three editions. The analysis considered the dimensions of the paper, the boundaries of the text area, the image frame, and the arrangement of elements within each illustration. The central research question was: What proportional systems and relationships can be identified in the pages of the illustrations in the three lithographic editions, to what extent do they correspond to systems such as the golden ratio, and what similarities and differences can be observed among them in terms of proportions? The study also explored the potential of geometric constructions to clarify the spatial organization of the illustrations.
Methods: The research employed a qualitative approach using descriptive-analytical and comparative methods within the framework of geometric analysis of composition. The research samples consisted of three lithographic illustrations depicting Zahhak in the aforementioned editions. Their shared narrative subject provided a consistent basis for comparing page structures and the arrangement of visual elements. The analysis focused on proportional relationships among the paper format, text area, image frame, and internal composition of each illustration. Geometric grids and the golden spiral were experimentally superimposed on the images to investigate possible correspondences between their dimensions and established proportional systems. The resulting configurations were examined and compared to identify similarities, differences, and distinctive features in the geometric organization of each page. The analysis also considered how these constructions could help identify potential focal points and possible paths of visual movement. These geometric models were treated as analytical tools for describing and comparing the illustrations, rather than as conclusive evidence that their designers had consciously applied specific mathematical principles.
Findings & Results: The findings revealed that the three illustrations did not follow a single, uniform proportional system. Instead, each edition displayed a distinct configuration of proportional relationships among the page components. In the Bombay edition of 1266 AH, the proportions of the text block approximated the golden ratio, whereas the image frame was nearly square. This difference indicates that the text area and pictorial frame exhibited distinct proportional characteristics within the same page. In the Tabriz edition of 1275 AH, the ratio of the paper's dimensions approximated the golden ratio, while the image frame approached a proportion based on the square root of three. The text area, in turn, approximated a proportion based on the square root of two. These findings demonstrate the coexistence of different proportional relationships at multiple levels of the page, rather than the consistent application of a single ratio throughout the composition.
In the Tehran edition of 1322 AH, the ratio of the paper's dimensions approached 4:3, while the image frame approximated a proportion based on the square root of two. This configuration differed from those identified in the other editions, particularly in the relationship between the paper format and the text area or image frame. The experimental application of geometric grids and the golden spiral facilitated the examination of spatial relationships, possible focal points, and potential paths of visual movement within the illustrations. The comparison also demonstrated that proportional relationships could differ between the overall page and its individual components. Although some dimensions approximated recognized geometric ratios, these numerical and visual correspondences alone cannot establish that the artists deliberately employed the golden ratio or other mathematical systems. Overall, the findings provide a comparative account of the geometric organization of the three illustrations and demonstrate the analytical value of proportional measurement for examining page composition in Qajar-era lithographic editions of the Shahnameh.