Proportions in architecture have always been of special importance and are considered one of the main pillars of designing and constructing buildings. Proportions mean balanced and harmonious relationships between the different parts of a building. The history of architecture, from ancient temples to modern buildings, has always witnessed the profound influence of proportions, and It has always helped shape architectural identity and, by creating a deep connection between humans and the environment, provides a lasting experience for residents and visitors. During the Qajar period, Kermanshah was one of the important and strategic cities in Iran, recognized as a significant commercial and economic center, and it has valuable Qajar-era houses. This research uses a quantitative approach and a descriptive-analytical method with the aim of determining the proportions used in the construction of courtyards in residential houses of the Qajar period in the city of Kermanshah, seeking to answer the question: Which of the common proportions in Iranian architecture do the proportions used in the construction of historical Qajar-era houses in Kermanshah, in the façade walls and courtyard dimensions, follow? The sampling method in this study is criterion-based purposive sampling (Criterion Sampling), in which 8 historical houses were selected. The innovation of the above research can be considered as the lack of analysis of proportions in Qajar houses in Kermanshah, as well as the use of geometric analysis in addition to numerical analysis. Based on the conducted studies, it has been determined that in Qajar-era houses in Kermanshah, there is a preference for using Iranian golden ratios over the classical golden proportions. And architects have made the use of Iranian golden proportions the main standard for building traditional houses in Kermanshah. Also, among the Iranian golden proportions (square, √1.25, √2, √3, and √4), the √1.25 ratio appears 87% of the time in house plans, and the √2 ratio appears 50% of the time in house facades, making them the most frequently used proportion patterns in the architecture of Qajar-era houses in the city of Kermanshah. This meaningful repetition can be significant for architects and restorers and may indicate a kind of compatibility and harmony of these proportions with the culture and architectural fabric of the city of Kermanshah from their perspective.
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