Study of numerical patterns and hidden order in traditional Iranian four-porch houses: A case study of the Tabatabai house in Kashan

Traditional Iranian architecture, particularly during the Islamic periods, has always been imbued with a hidden internal order rooted in numerical concepts, sacred geometry, and principles of proportionality. The four-iwan house typology is one of the most notable manifestations of this architecture, featuring a harmonious and meaningful structure where aesthetics, functionality, and climatic responsiveness are intertwined. This qualitative and analytical study investigates the numerical patterns and hidden order in the Tabatabaei House in Kashan, a prime example of four-iwan traditional houses. Through field observations, geometric analysis of plans, spatial proportion evaluations, and comparison with theoretical foundations of Iranian-Islamic architecture, the findings reveal that the hidden order is based on systematic geometry, specific numerical ratios (such as ۱:√۲ and the golden ratio), and repetition of symmetry-based patterns. These results contribute to a deeper understanding of vernacular architecture and offer inspiration for contemporary design grounded in traditional principles.

کلیدواژه ها:

Traditional Iranian Architecture ، Four-Iwan House ، Hidden Order ، Golden Ratio ، Tabatabaei House ، Sacred Geometry