The Ratio of Length to Width in the Main Spaces of Traditional Houses of Yazd: A test for Pirnia’s Statement on Iranian Golden Rectangle

There are explicit suggestions in Mr. Pirnia’s teachings on the traditional Iranian architecture that refers to a so-called “Iranian Golden Rectangle”, especially when he speaks about Iranian houses. He calls a rectangle circumscribed in a regular hexagon the Iranian Golden Rectangle. This rectangle has a ratio of length to width of 1.732 or ?3. He indicates that Iranian architects used to use this rectangle widely when designing central courtyards of houses and the rooms surrounding the courtyards as well. He claimed more exactly that the courtyards and the rooms getting light from their longer side have the ratio of this rectangle, while the rooms getting light from their shorter sidehave the ratio of half of this rectangle i.e. 1.154. He didn’t give any further explanation or examples for his claims. There have been some other well-known scholars who have repeated this statement within their writings again without presenting convincing evidence. This article aims to test this hypothesis in traditional houses of Yazd city. The most important reason why to choose Yazd is that it was the birthplace of Mr. Pirnia where he lived for several years. So, it seems probable that his opinion of Iranian Golden Rectangle was shaped as a result of his attitude to this city’s architecture. In order to accomplish this research two sets of samples were gathered. One set consisted of architectural drawings of 17 houses that were obtained consultingtwo reliablepublished resources. The other was provided using the oldest aerial photos of Yazd city taken in 1957. From these photos the ratios of 166 courtyards were extracted. Next, a statistical analysis was done to test the hypotheses set forth by Mr. Pirnia. Assuming that the ratio of lengths to widths are distributed symmetrically around a constant figure and follow a normal distribution, a statistical analysis was done.The results of this test clearly rejected Mr. Pirnia’s hypotheses. Then the authors’ analysisis set forth. To come to a real understanding of the way the architects determined the ratio of the spaces of houses one should consider the real context within which the architects accomplished their projects and the many limitations they should dealt with that made it unjustifiable to insist on using oneinvariable ratio. After scrutinizing the diagrams of ratios produced,the author’s deduction is that there were some preferred ratios that architects attempted to stay close to when designing specific spaces of houses. They believe that architects used to use some simple "arithmetical"ratios e.g. six to five or eight to fivein order to reach this aim rather than using more complicated "geometrical" schemes.Besides, there is some historical evidence regarding the methods Iranian architects used to use when designing the horizontal plan of buildings that approves this conclusion. At the end of this article some suggestions are made for furtherfuture research on the pre mentioned statements of Mr. Pirnia and also concerning some findings of current research.