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Purpose: 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. Methodology: 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. Findings: 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. [ABSTRACT FROM AUTHOR]

Liquid storage structures represent an important component of modern infrastructure. They can take variety of shapes of which the conical shape is one of the most common configurations. Conical tanks are preferred by both architects and structural engineers because of their appealing look and structural efficiency in addition to their large capacities with relatively small footprint area. The state of stresses in these tanks is rather complicated and needs powerful computational tools. However, in the preliminary design phase, it is important to have a simplified analysis method for selection of economic design parameters including tank height, inclination angle, and footprint radius needed to achieve the desired tank capacity. It is also of importance that the structural engineer has an insight and understanding of the effect of these various parameters on the resulting internal forces acting on the tank. This paper presents a simplified analysis of conical tanks under hydrostatic loading based on the application of the membrane theory. The equations governing the behavior of these structures are first derived. Then, they are applied on several vessels of practical dimensions and the resulting of stresses are presented to give a deeper understanding of the resulting internal actions. Moreover, a simple guide to achieve efficient structural preliminary design parameters for a wide range of tank capacities is introduced.