Mathematical Analysis of Simple Karbandy in Iranian Architecture

In this article, understanding of Iranian architecture can be considered as art and mathematics, but unfortunately less to study architecture, the mathematical components of these elements have been analyzed in terms of art. Karbandy or Ribbed Vault consisting of curves with arches geometric rules specified under the original cover intersect and appear to pose is a covering structure. Another definition of Karbandy is a simple circular motion from the rafters in the form of a circle. In the 3rd century A.H., the Mosque of Shiraz (262 A.H.) in case we find that although the Karbandy no more corners of interpretation (which is to give the dome on it there) but its form, like complete “Karbandy”, and in fact, an introduction to the beginning Karbandy. Also, we can see a full example of Karbandy in dome of Nain Mosque in the 4rd century as well as an example of “Barber” and create of the main cover. Karbandy cases is named as Karbandy in bedchamber of the eastern dome of Nizam al-Mulk Mosque in the fifth century, after that in the 6rd century it is easily seen under the dome of the “Chehel Dokhtaran” building and dome of Sheikh Junaid at the Turan Posht village of Yazd. From the 7rd century hitherto now, Karbandy gradually was used in conjunction with the creation of architectural space as independent of sturcture. Unfortunately, the oldest written document about Karbandy being a draw on the scrolls belonged to the architecture texts of Akbar Mirza Qajar. The use of mathematics as an international language and understandable for everyone is the best way to reach a common cognition of the Karbandy. The studies show that regarding to the perfectly grammatical and legal nature of Karbandy, the mathematics can provide a complete base for reading it. This research can be considered as an objective and applied research that is done on studying the data collections gathered from written methods in the books, library-based manner and reviewing the cases that had not been registered. The research method is a descriptive, analytical and logical reasoning. Regarding to the several parameters of Karbandy, they can be separated into its components that a mathematical model was presented for each factor. After reviewing the material presented in the analysis, they show a mathematical model of simple Karbandy examined there and it was found that their formula replaces all types. This research shows that four factors is contributed to the formulate and model Karbandys. Their factors include N (sides Karbandy), D (distance connection), θ (vertical or non-vertical) and background factors (C1, C2, ..., Cm). There are other factors but these four factors are important that can help formulating and mathematical modeling th all of Simple Karbandys. Generally, we have two main methods for drawing Karbandy listed below: The Method of Pirnia and Manner of Sherbaf. In the method of Pirnia is shown that for drawing the circle, first, the circle should be divided, then it is splitted in connecting points, and finally it should be done on the the field. In the manner of Sherbaf, it is performed by drawing it on the access point. Therefore, on the base of every drawing, Karbandy is different and varied. Numerous examples of outlining the methods provided in the nodes and Karbandy to follow the outline of the presentation will be avoided in this abstract.