A new approach to the geometric modeling of Iranian domes

In Islamic architecture, using arches to build dome-shaped buildings has been very common. So, the research on building the domes of shrines and mosques is undoubtedly directed at studying the arches of those buildings. In this article, we will investigate and geometrically model the domes from the perspective of differential geometry and as a rotating surface. We try to present the scientific connection between the art of architecture and differential geometry in a way that interests experts in both architectural and mathematical trends.

In architecture, the dome is the product of a productive cycle around the vertical axis. This interpretation is equivalent to the definition of the rotating procedure (generating curve) in the subject of differential geometry. Special methods can obtain the generator curve. At first, according to the drawing method, we parametrize half of the arch in the Euclidean xoz plane according to the length of the dome opening and then rotate the resulting curve (or the generating curve) around the vertical z-axis. The method of conducting this research is quantitative and includes calculations related to the types of domes, and its type can be considered descriptive research.

We found a significant link between the mathematics that governs domed buildings and the productive arch.

Originality/Value: 

Considering the multitude of types of arches in architecture, in this article, after stating some necessary definitions of differential geometry, in addition to presenting the method of drawing each arch, we will only bring the calculations related to the types of arches with legs, horned goats, five-o-seven and shamrocks. Ultimately, we will implement our calculations on the dome of Juma Mosque in Ardabil.