Analysis of theoretical and practical geometry of Abbasi jame Mosque's discontinuous double shell dome

Geometry, meaning the knowledge of size determination, can be considered as a hidden and evident architectural style of various periods that have been used both from theoretical and practical aspects in the construction of buildings in the past. Considering the importance of geometry in art and architecture, research on geometric principles shaping architectural works can be considered an important field for study. One of the special structures that Iranian architects have made a lot of effort to create is "Dome" which is one of the most important elements of Iranian architecture. The dome has special features that distinguish it from the arch. Some of the most important of these features are the sign, the prominence and the appearance of distant distances. For including these features the dome have to hold specific concepts, such as the depth and breadth of the span, the concepts that affect the geometry of the plot and the proportions of the building. Double shell discontinuous dome is one of Iranian domes, in which most of the features mentioned are found together. These domes are diverse in terms of geometric form and construction techniques. This variety and abundance has made many aspects of the geometry and the technology of these buildings still unknown, which need to be studied. The necessity of this discussion is significant from two dimensions of theoretical geometry and practical geometry. Today, due to the very limited information of the past ideas and techniques, it is necessary to draw out theoretical geometry by analyzing practical geometry in buildings. Studies on discontinuous double shell domes mostly indicate their stylistic and structural characteristics and in terms of geometry there are lack of researches. The present research is an attempt to find the answer to these question: what is the relationship between theoretical and practical geometry in design and construction of discontinuous double shell domes? What are the main factors affecting discontinuous double shell domes design and construction process? To answer questions, the theoretical foundations of geometry usage in Iranian architecture were investigated. Then, the study was carried out on the case study and applying principles extracted in the theoretical part and finally the geometric process which forms the building was decoded. This research aims to explain the way of implementing theoretical geometry and transforming it into practical geometry. Findings show that the design and construction process follows a predetermined design system in which the principal forming shapes are square, circle, and pentagon and the proportions of the components are also based on golden ratio(Ɵ), so the proportions apply to the plan, cross section, and facade. Also knowledge and ability of architect in theoretical and practical geometry has been the main factor in design and construction process of these domes in Iran. The results can be beneficial in restoration and rebuilding of domed buildings specially in cases that some parts are missing and there is lack of documentation. Also as the results help to reading out the Iranian vernacular knowledge, would be effective in design and construction of modern shell structures.