Geometry and proportions are considered fundamental principles of Iranian architecture and have played a significant role in the spatial organization of historical houses in Qom, especially during the Qajar period, late Qajar period, and Pahlavi era. This research aims to conduct a comparative analysis of spatial proportions in 23 historical houses in Qom, extracting the dimensional ratios of the main spaces (courtyard, room, three-door, and five-door) and examining their compatibility with three recognized proportion systems (the golden ratio 1.618, the Iranian golden rectangle 1.73, and the Guz and Paymon 1.066). The research method is analytical-comparative, and data were collected through field measurements and a review of accurate maps. The data were then analyzed using statistical tests of variance analysis and one-sample t-test in R software. The findings indicate that the general principles of proportions have maintained relative stability across the three periods; however, different spaces have shown varying degrees of compatibility with the examined proportional systems. During the Qajar period, rooms aligned most closely with all three proportion systems, whereas in the late Qajar period, reception areas predominantly aligned more with the golden ratio. In the Pahlavi era, courtyards again showed a tendency towards Gaz and Peymoon, likely reflecting standardization considerations during this time. On the other hand, the non-adherence of courtyards in the Qajar and late Qajar periods to the examined proportional systems, unlike the internal spaces, may be due to land limitations, changing living needs, and socio-economic transformations of that era. This research emphasizes the importance of recognizing traditional geometric principles in contemporary architecture and suggests utilizing the achievements of these proportional patterns to sustain local identity in the hot and dry climate of Qom.
