typology and the formulating geometric structure of karbandi in iran's architecture

the transition of a squared surface to a spherical one is one of the important issues of construction in the world architecture history. the combination can numerously be observed in the iran's architecture prior to the islamic period. for instance, the palace of shapur (a king) which was splendid and daring palace had a ceremonial court and featured a parabola dome. chahar taq (four arches) is also another example of this pattern. the building term of chahar taq is originally a square construction including four arches in which the interior space is normally covered with a dome placed on tromps. the domed room during the islamic era gained a great position and completely replaced the columned shabestan during the seljuk period. the domed room building pattern can be separately categorized into three different areas for iranian architecture during the islamic era as follows: 1. square area, 2. transitional area, 3. dome. due to the numerous uses of the aforementioned pattern, the architecture of these three areas became highly developed and consequently the transitional area diversely expanded and various methods were innovated. among these methods mentioned above, we can name some transitional ones like flat trompe, trompe, patkane, muqarnas, pendentive, squinch, vaulting and karbandi. among them , karbandi is the most advanced transitional style and one of the genuine and old patterns of iranian architecture which is resulted through iranian architects' understanding of geometry and advanced mathematics. contemporary researches about the relation among mathematics, geometry and iranian's art indicate that iranian muslim artists had significant progress in geometry and mathematics in the mid- centuries. according to authors of these lines, karbandi is one of the prospects of such progressions in geometry and mathematics. recreation of this pattern necessitates sufficient understanding of all aspects of the subject such as typology, recognition of geometrical features, structural and executive characteristics. in this regard, applying a rational order, this paper has tried to consider typology and develop the authentic grammar of karbandi geometry following aforementioned sparse essay of karbandi. the method to achieve the purpose of study is that we model real cases by computer and separately create from each one a utilizing plan of geometry and then formulate geometric structure of rasmi karbandi in the form of geometric or arithmetic scheme by organizing these figures. whereas this study done by schematic mathematical systems and largely dependent on logical reports can be mentioned that the research method of this study is a logical argumentation one. this paper has first accounted for the history of typology, then the definition of specialized terms and lastly the typology of different kinds of karbandi respectively. one of the findings of this study is developing the geometric structure of rasmi karbandi that has the ability to organize all related cases. other achievements are to introduce and name compound rasmi karbandi, special rasmi karbandi and also present non-simple karbandi and five branches of it, namely, duplication, mounted, dual arch, extension and endogenous karbandi that have been studied in detail.