Geometrical Analysis and Numerical proportions in the decorations and physical composition of Pir Bakran mausoleum

Pir Bakran Mausoleum is the Tomb of Mohammad Ibn Bakran, one of the ascetics of Sofia which high ceiling is a link between the old man of wisdom and the sky. Pir Bakran Mausoleum is located in the city of the same name, 25 kilometers southwest of Isfahan. The tomb is one of the works of El-Jaito period (Soltan Mohammad Khodabandeh) and is located near the old Jewish cemetery of Isfahan and the holy Jewish cemetery (Astrakhaton). According to the inscriptions, Pir Bakran tomb was built between the years 703 (the year of Mohammad bin Bakran's death) and 712 AH.
This building is one of the masterpieces of Ilkhani architecture. In the physical structure and decorations of this building, plasterwork with various plant motifs, tile decorations, moqrans and wall paintings have been taken. These decorations have been used to form a variety of plant, geometric, written and composite motifs. The purpose of this research is to investigate the wisdom of the origin of geometry and decorations in the Pir bakran tomb based on an analysis from the perspective of the Qur'an and traditions, the symbology of geometric shapes, the wisdom of the numbers used in the tomb based on the science of letters.
This research tries to answer these questions: 1- In which parts of the building and in what form did semantic decorations and geometry appear? 2- What messages do the decorations and geometrical shapes in different parts of Pir bakran tomb carry?
The research method is qualitative and descriptive-analytical based on library studies, documents and field studies of Pir bakran tomb inscriptions. The steps of the research method are as follows: first, field visits were made to the building and the construction periods of different parts of the building were separated; After that, the geometry of the spaces was evaluated and an attempt was made to understand the wisdom of their architecture by analyzing them. Also, by using the science of numbers and alphabets, an attempt was made to find a logical connection between the spaces. By analyzing the concepts of the inscriptions, an attempt was made to express their wisdom; Also, by studying the old photos and old maps prepared by Ernst Herzfeld and comparing it with the current situation, the restored and filled parts for the protection of the building were identified.
The results of the research show that the concepts and meanings are in the form of geometry (such as turning a square into a circle), religious forms in the majority of blue sun and crucifix tiles, linear decorations and the use of divine verses and plant plasters, related to the use of each part of the building has emerged. The use of sacred numbers (4, 9 and 11), symbols and religious forms in the spatial and physical formation of the building has caused a spiritual connection between the earthly world (material) and light (spiritual) and the architecture of the shrine tries to reach the essence of earthly man. To display the sacredness of the Lord, which is the main goal of dervishes.