Geometric Morphology of Islamic Mosques Courtyards in Iran (Comparative Examples: 9 Mosques from Timurid, Safavid and Qajar Periods)

Places of worship, especially mosques, are considered one of the richest platforms for the evolution and exaltation of the human spirit and possess great significance. The geometry of these buildings is considered one of their common and regular features, having specific proportions and rules. Also, it has created an intangible heritage identity for the contemporary era. Knowing and interpreting these proportions can play an important role in repairing and reusing the historic building, using them in future architectures, and elevating the new architecture. This research aims to discover similarities and differences between cultural platforms from the Timurid to Safavid eras by reviewing the principles and proportions using geometric analysis. To identify the mathematical relationships of the architectural body of mosques' courtyards and understand their geometrical proportions, this research has used the combined method of historical interpretation based on valid evidence and logical reasoning of the mathematical type. Based on this, the sides and proportions of the courtyards and constituent parts of 9 Timurid, Safavid, and Qajar mosques have been subjected to numerical analysis based on Euclidean-longitudinal calculations and the scale of proportions in the courtyard plan of the mosques. Findings of this research indicate that the geometry of the courtyard and components of the discussed mosques have employed golden proportions, and Mahtabi halls attached to the mosque courtyards during the Safavid period have been developed in the same proportions through the Qajar period.