Unlocking Sinan’s Architectural Language: Modular Design Through Geometric Recursion

Abstract This study investigates the possibility that Architect Sinan employed a recursive geometric modulation system—rooted in the use of the circle and the square—in the design of his architectural masterpieces. Through detailed proportional analyses of the Privy Chamber of Sultan Murad III and the Selimiye Mosque, the research explores how a series of circles correspond precisely to critical structural and spatial elements of the buildings. Following these two examples, the Haseki Hürrem Bath—one of Sinan’s early works—was examined within the context of ad quadratum to further test the study’s approach. The results reveal a design methodology so deliberate and consistent that it cannot be attributed to coincidence. These findings suggest that the recursive application of modular circles and squares may have served as a foundational design tool, guiding both the aesthetic and structural logic of Sinan’s architecture. This research emphasizes geometric discipline over speculative symbolism, proposing that Sinan’s mastery lay in a refined system of modulation.