Explanation of Geometrical System of zone of transition in Gonbad-e Sorkh in Comparison with Common Pattern of Seljuk's Zone of Transition

Changing the square into the circle in the structure of dome chambers was a main problem in Iranian architecture. The solution to this problem has led to the formation and creation of capable methods and techniques in the structure of a part of dome chambers that changes square chamber below into the round dome above it. This phenomenon has been considered as "the zone of transition" (transitional zone) in many studies on Iranian architectural history, but it has been less seriously studied in a strict sense as an important independent part. On the other hand, the way square chamber corners corbel has made different forms of structures that is called "squinch". The four squinches together with the middle parts between them organize the mentioned zone (zone of transition). In some studies, the zone of transition has been described considering the load-bearing elements of corbelled form of squinches. Some experts have indicated different forms of squinches such as "stalactite squinch", "conical squinch", "trie-lobed squinch","squinch net" and some others have talked about it considering materials, ornaments and constructional styles. Although these considerations present some aspects of transitional zone such as historic, structure and form, it rarely has been explained as a complete evolution and clear classification. Geometry, as the essence and nature of this process (changing square into the circle), is certainly a decisive item. Therefore, this research is going to explain the zone of transition from the view point of geometry, considering the geometrical system between square and circle that leads to a regular polygon as the base of dome. According to this geometrical approach, the article first reviews two old methods used before Seljuk era and then, explains the elegant form of Seljuk zones of transition originated in Nezamolmolk dome of Isfahan, as the most fashionable pattern existing in Iran for more than three centuries. In the next phase, which is the context of this research, the transitional zone of Gonbad-e sorkh is explained as a novel form leading to a hex decagon. Although the dominant pattern also eventuates a hex decagon, the case of Gonbad-e sorkh, as an authentic Seljukian monument, does not follow it and presents a different solution. The difference between these two solutions is presented by a comparative analogy. First, the process of changing square into octagon and then hexadecagon in Seljukian fashionable pattern is described. Then, it is compared with the process of changing square into hexadecagon in Gonbad-e sorkh. By this comparison, the paper finally presents the zone of transition of Gonbad-e sorkh as a "shortcut pattern" of a novel geometrical arrangement of transitional elements.