An Approach to The Geometry of Persian Domes; The case study of Shah Nimatullah Vali shrine

Abstract Sometimes, history comes to us through historians and sometimes true artists. Creating masterpieces such as paintings, carpet weaving, sculpturing, and architecting eye-catching buildings, were among the ways artists of the past used to convey their beliefs and the history of their regions to the future generations. Therefore it is necessary to maintain the link between past and future generations by protecting and restoring these works. Mathematicians claim that one of the most efficient ways for this purpose is to know the geometric features of the relics. In this article, we will research a type of historical building i.e. domed roofs specially. The fundamental properties of these structures are based on the fact that they had been built by rotating a generating arc around the vertical axis called Shahang on a foundation called a drum. This concept is analogous to the definition of the surface of revolution in differential geometry. Modeling domes by using this concept and performing mathematical calculations on them, provides us with detailed information about the behavior of these structures. As an example, we are going to investigate the cause of the collapse of a part of the dome of Shah Nimatullah Vali shrine, by using mathematical tools.