Abstract

This study adopts an analytical–comparative approach to investigate the structural and philosophical foundations of geometry in Safavid architecture and the grid system in modernist graphic design. The primary objective of this research is to identify the shared principles underlying spatial organization and to explain the fundamental differences in the intellectual origins of these two visual systems. The findings indicate that despite the temporal and essential distinctions between these two approaches, both systems are grounded in mathematical logic, precise proportions, and grid-based structures. In Safavid architecture, the system known as Peymoun functions as a modular and constant unit responsible for establishing harmony between the whole and its constituent parts; in this respect, it demonstrates a significant structural similarity to the “modular grid” in modern design. Both systems employ stable mathematical proportions, such as root-two and root-three rectangles as well as the golden ratio, in order to achieve balance, equilibrium, and visual harmony.

Nevertheless, the analytical results reveal fundamental differences in the intellectual and philosophical dimensions of these two approaches. Safavid geometry serves as a means for manifesting metaphysical concepts and expressing the movement from “multiplicity toward unity”; through intricate ornamentation and the symbolic representation of forms such as the dome, it guides the viewer’s mind toward the sacred realm. In contrast, the modernist grid system emerged from a rationalist and industrial worldview that, through emphasizing objectivity, the elimination of ornamentation, and the prioritization of function, seeks the clear, rapid, and precise transmission of information within modern societies. Ultimately, this study demonstrates that geometry, as a universal language, constitutes the foundation of visual credibility and the enduring quality of works in both traditional and modern approaches.



Keywords: Safavid Architecture, Grid System, Applied Geometry, Modernist Graphic Design, Mathematical Proportions