Geometric Analysis of the Historical Periods of Architecture in the Mausoleum of Shah Nematollah Valli in Mahan

This paper analyses the mausoleum of Shah Nematollah Valli in Mahan. Its construction started in the Timurid era and gradually transformed into its current form. This complex has been built during three periods (Timurid, Safavid, Qajar) and in a variety of Iranian architectural styles. This article tries to recognize the architecture of different periods from the point of view of proportions and geometric order. The method used in the present study is analytical-descriptive in accordance with the research hypothesis. To achieve the theoretical foundations of the research, which includes information about geometry and proportions as well as similar examples, data is gathered from previous resesrch and field works then data is analyzed through the descriptive and analytical methods of building geometry. Different spaces of this complex are evaluated in terms of compatibility with golden ratios and geometric patterns using software such as phi Matrix 1.16 pro and Phi Matrix Golden Ratio. According to the obtained outputs, the initial geometry of the building in the Timurid era, in comparison with its later geometry in the Safavid and Qajar periods, has undergone ruptures and changes in pattern (paradigm shifts), although there are similarities. The results of this study show that the initial geometry of the building follows a precise geometrical regularity in terms of form in the dome part, has the form of a Chalipa enclosed in a regular octagon in the plan, and has golden rectangular proportions in the facade and section. Furthermore, the geometry of the added parts in later periods is based on square shapes and a quadruple system.