Reinterpreting Courtyard Geometry through Qur’anic Principles: Mizan and Tadabbur in Mashhad's Transitional Houses

Aims: This study is grounded in a Qur’anic hermeneutic framework that interprets spatial design through the principles of Mizan (divine balance) and Tadabbur (contextual adaptation). Within this perspective, we examine the central courtyard as the socio-environmental core of traditional Iranian houses. While the central courtyard is established as the socio-environmental core of traditional Iranian houses, the quantitative link between its geometric proportions and spatial adaptability remains insufficiently explored. Methodology: To address this, we employed an integrated hermeneutic-quantitative methodology. The research involved the digital reconstruction of 20 historically significant transitional houses in Mashhad, followed by geometric and configurational analysis. Framed within a post-positivist paradigm and employing a quantitative-correlational approach. Finding: Findings from a simple linear regression analysis (N = 20) confirm a statistically significant linear relationship between these indices (R² = 0.89, p < 0.05), expressed as y = kx. The coefficient k declined from 1.70 (Qajar) to 1.28 (the Second contemporary- pahlavi period), signaling a weakening of the geometric-spatial over time. Conclusion: This quantitative shift as a manifestation of Tadabbur—a pragmatic adaptation to urbanization pressures—which nevertheless moved away from the ideal Mizan embodied in Qajar-era proportions. Therefore, this study serves as a translational framework, proposing that the historically optimal coefficient range (k≈1.2−1.7) be translated into a modern design parameter. Contemporary architects can restore environmental and psychological resilience by stabilizing this coefficient, re-centering the courtyard as the adaptive, sustainable, and soul-nourishing core of modern Mashhad homes. The research thus offers a culturally-grounded, evidence-based model for reintegrating traditional spatial wisdom into contemporary sustainable design.