Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 2008-5621) Vol. 13, No. 3, 2021 Article ID IJIM-1427, 17 pages DOR: http://dorl.net/dor/20.1001.1.20085621.2021.13.4.6.5 Research Article The Impact of Geometric Proportions on Daylight Performance and the Proportions Derived From Nature in Traditional Houses (Case study:Ardabils Houses) M. Javadi Nodeh ∗ , A. Shahcheraghi †‡ , AR. Andalib § Received Date: 2020-03-11 Revised Date: 2020-07-03 Accepted Date: 2020-09-26 ————————————————————————————————– Abstract The use of proportions derived from nature in traditional architecture is a constant principle in the interactions between structural and physical environments. It has been shown that having an intrinsic relationship with nature can lead to formal similarities. This study attempts to determine the com- patibility of common geometric proportions used in traditional houses with daylight performance and natural proportions of the surrounding physical environment so as to recognize the most compatible structural layout with nature. To this end, 28 Shahneshin rooms were chosen from 21 traditional houses in Ardabil. The required data were collected via field observation and logical reasoning and then numerical analyses were conducted on them. After that, using frequency diagram and mean coefficient of variation, the distribution pattern of the proportions employed in the Shahneshin rooms were determined. Finally, the compatibility of geometric proportions and skylight characteristics with daylight perimeter zone was examined through numerical analyses. The results obtained from the most common structural layouts indicated that in traditional architecture, physical environment and structural environment were compatible and interacted with each other; 95% of the prevalent pro- portions in the traditional houses of Ardabil appeared to follow arithmetic ratios and many of them were found to follow golden proportions. Moreover, they were observed to have the highest level of overlap with the frequency distribution and perimeter zone of daylight. Furthermore, the analysis of no-sky line area showed that in all of the cases, sky was visible from the inner space of the rooms. Keywords : Geometry; Nature; Proportions; Daylight Perimeter Zone; Traditional Houses; Ecological Architecture. —————————————————————————————————– * Department of Architecture, Faculty of Civil, Archi- tecture and Art, Science and Research Branch, Islamic Azad University, Tehran, Iran. † Corresponding author. Shahcheraghi@srbiau.ac.ir, Tel:+98(912)3290241. ‡ Department of Architecture, Faculty of Civil, Archi- tecture and Art, Science and Research Branch, Islamic Azad University, Tehran, Iran. § Department of Urban Development, Faculty of Civil, 1 Introduction T here are two general approaches regarding the relationship between structural and physical environments: ’intrinsic and conceptual relation- Architecture and Art, Science and Research Branch, Is- lamic Azad University, Tehran, Iran. 261