Journal of Researches in Islamic Architecture

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In traditional architecture, the adherence of architects to the rules and proportions in numbers, geometry and music is present in designing and shaping many public monuments, and mathematical proportions, artistic ratios, or musical proportions are used in geometry of these buildings. Extracting and matching mathematical rules and proportions and examining them in the architecture of the traditional buildings are among complex issues which are well-worth for further analysis. The present article is aimed at finding the link between «architecture and music», «architecture and mathematics» and «music and mathematics» and determining the boundaries and mutual points of these sciences. The objective was to reorganize geometric pattern in Jelokhan of Sheikh Lotfollah Mosque in city of Isfahan and the linkage of its Asemaneh of the dome with music. This is a theoretical research and its theoretical basis is carried out with a historical interpretation method. Logical reasoning has been used in investigating Jelokhan and Asemaneh of Sheikh Lotfollah Mosque in Isfahan. In order to fulfill the purpose of the sudy, the relations between «architecture and music» and «architecture and mathematics» were analyzed in the form of a concept as «music-math» in architecture for adaptation. In examining the relationship between architecture and music, the researchers faced many stances. For instance, some authors believed that architecture is an expression of music in its further development or in its evolution, while some others indicated that architecture is the frozen music in space. Thus, to understand the relationship between music and architecture, you need to understand the language of both along with finding their mutual ties. Therefore, in extracting common principles and characteristics that include criteria, similarities and symmetries while keeping in the mind the relative importance of measuring the relationship between architecture and music, we analyzed it in terms of rhythm, equilibrium, balance, symmetry, high and low points, decoration and beauty of decorations, color, hearing sensation, pleasure, and quantitative role of numbers. In examining the relationship between architecture and mathematics, math is also considered as the purest type of thought and one of the main causes of human closeness to God. That is probably why most traditional architects bring math ideas into architectural designs so as to verify their beliefs about the Creator and the natural world around us. Mathematical expressions in architecture can be expressed numerically, symbolically, philosophically, creatively, conceptually through numerical ratios. Finally, in explaining the concept of «music-math» in architecture, we need to determine the extent to which musical and mathematical uses of architecture are parallel, shared, and reciprocal. In scrutinizing the proportions between architecture and music, architecture and mathematics, principles and common standards such as equilibrium, balance and symmetry, decorations and proportions, hearing sensation, numerical philosophy, numerical proportions, graphic geometry and numerical relations were obtained. In order to elucidate the theoretical findings of the research which are explained by the relation among the concepts of music, mathematics and architecture, we focused on Jelokhan and Asemaneh of Sheikh Lotfollah Mosque in Isfahan. The discovery of a hidden geometry in the depth of Jelokhan combined with Iranian Dastgahi music and mathematics along with finding a harmonic pattern in abstract patterns of the dome of Asemaneh coincided with changes in the frequency of the notes reflects its architect›s adherence to the principles of music and math in the architecture of this mosque. The proportions and rules contained in the musical, architectural, and mathematical Jelokhan of the mosque were analyzed through the fact that most geometric points of Jelokhan from the beginning to the end, the main lines, the lines of symmetry, the vaults, the lines of the Mogharnas, and many of the details of the mosque›s Jelokhan were built based on a pattern which is formed in a modular compendium of mathematics and music using the similarity of the Shur-e Sol Dastgah. Besides, the beautiful harmony of this Iranian Dastgah is seen in Jelokhan of the mosque and the walls of the Naghsh-e Jahan Square. In addition, the harmony of this Dastgah is present in heavenly decoration of mosque’s Asemaneh; decorations that, similar to orthogonal mathematical models are aggregated or opened. These harmonic decorations are a certificate of fine and delicate musical notes or an increase in the frequency of notes in Shur Dastgah.

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Problem statement: The concept of resilience has long been published to explain how different types of systems respond to unexpected shocks, and research on resilience of environments to abnormal hazards has just begun, requiring extensive reflection and consideration. Spatial resilience thinking is as one of the new dimensions in the field of resilience and architecture. This dimension seeks to address the issue of the vitality and dynamics of the architectural space by preserving identity and function through attention to specific characteristics and capabilities of the space over time versus gradual and slow disturbances. resilient space as the appropriate context for possiblity continued vitality provides dynamic while maintaining performance; It shows little vulnerability in the face of crises over time by the spatial capabilities, and responds to changing conditions through adaptation to the needs and demands of the society, and satisfies spatial users' satisfaction with different tastes and guarantees and sustains the vital system of space. But most of the newly constructed spaces are vulnerable to crises and lose their efficiency quickly and the users of space leave and vacate; Therefore, the historical bazaars of Iran, as one of the valuable spaces that have continued to operate despite changes in different periods and have been able to meet and provide the suitable body for the needs of the day, are remarkable. Therefore, to resolve part of this epistemic vacuum, the present study focuses on the limited domain of the Amir complex in the historical bazzar of Tabriz, considering its position and role in the life of the Bazzar Tabriz has paid off to the rooting of the resilience of this space and examining its spatial capabilities. So this research seeks to answer the question of how resilience has been achieved in the historical space of Iranian bazaars? And how has the resilience of the Amir complex in the historical bazzar of Tabriz come about in light of the changes in recent years?
 

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The discipline of the structure of a complex has a direct relationship with the observance of hierarchy in it, because the architecture of mosques is no exception to this, and this principle has been observed in the structure of these buildings. The value of this sequence, in addition to creating spirituality in a non - verbal way, provides the ground for human excellence and leads him to his goal.
The importance of this sequence in accordance with the functional and physical characteristics is effective in strengthening the mental image of a person and he can feel this issue in a tangible way in different stages of passing from inside to outside the mosque. During his motion to the correctness Mosque of hierarchy caused him to Effect on his activities and the mental image formed in him to establish an emotional connection between him and the place, which is interpreted as a sense of place. The sense of place is formed to a degree that, based on the discovery and decipherment of the hierarchy created, will create a sense of remembrance and belonging. Sense of place is the product of human exchange with the environment and vice versa, which has a great impact on behavior and performance and will provide the basis for his familiarity with the surrounding place. The more physical symptoms in the environment, the better the viewer can relate to the environment.
Physical elements are so important that they can turn space into a place to show a new structure. The difference between space and place produces a character that the viewer can better understand by understanding the difference. Acquiring such cognition creates more permanence in the individual chr('39')s mind and creates a sense of place.
Components such as body, activity, and mental image represent the place model. The body is a representative of human tradition and thought that can organize the space. With the correct understanding of the body, space can be better understood. Grutter states that the body should be chosen to represent the content and idea of the design, and to express spiritual bodies, a suitable visual body should be chosen that is understandable, and these interpretations point to the importance of the language of the space body.
Codes received from the body are effective in orienting people in the environment. Without guidance in the environment, a person can be guided to the destination and reach the goal with his first presence based on perception of the body. It can be said that the person is constantly decoding in order to better understand the environment. Human interaction with the physical environment will tell him what behavior he has shown in the environment and how to take advantage of the non-verbal communication of the environment.
According to canter chr('39')s model, in order to better understand the physical elements, we turn it into three physical components: horizontal, vertical and opening, and analyze them. The analysis makes it possible to see the hierarchy in such a way that it understands the codes and signs manifested in it and based on the signs obtained from the hierarchy, its activity is as stillness, movement or Do silence with movement in the mosque.
The purpose of this study is to investigate the changes in the sense of place in mosques and the answer to the question how time has affected this sense in mosques? To study this question in more detail, the mosques of three historical periods of Qajar (Safar Ali and Seyed Hamzeh mosques), Pahlavi (Nabi Akram and Tabatabai Hakim mosques), Jomhuri Eslami (Vali - Asr mosque and Tabriz University mosque) were studied. In the research method section, the question is examined qualitatively and using library resources such as books, articles, technical documents of mosques and field work and by presenting a research model based on the physical form of mosques and evaluating it based on hierarchy and analysis of physical elements. Affecting the sense of place studied.
The findings indicate that some of the physical elements in the mosques have changed over time and this has diminished the physical richness of the hierarchies. In addition, the elimination of hierarchies in some mosques does not make sense of place and the user cannot perform the required activities in space That user inactivity will not provide the mental image needed to create a sense of place. The results show that change or elimination of hierarchy in Tabriz mosques with other parts of Iran was not unexpected because the difference in climate in Tabriz caused this difference On the other hand, hierarchies and sense of place in the mosques complement each other so that changing the sequence of hierarchies in each period causes the user activity to change from static to move less mental image of space and the link between the hierarchy. And it will diminish the sense of belonging.

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In specialized topics of aesthetics, structure and function, the buildings of Islamic architecture in Iran during certain periods, show the strong presence
of intellectual sciences such as mathematics. The use of geometry as a part of the science of numerical mathematics, which in its intellectual position has
complex calculations, indicates the connection of Islamic architects with the mathematicians of their time. According to the available books and written documents, the architect's personal reference to complex mathematical books in terms of numerical application is a subject that has been seen in lesser power. Accordingly, in this article, the educational relationship between architects and Islamic mathematicians has been examined. Geometry in its numerical position can not be transferred to the architectural structure, and this must be transferred to a specific geometric process in terms of action. How to connect the mathematics of Islamic theology and architecture about geometry, and of a special theoretical or practical type that can be used in the field of architecture is the basic question of research. How Islamic architects have understood theoretical and practical geometry from mathematicians and have applied it in architecture. In this regard, in the present study, the author has examined the research and analysis operations by identifying the fourth to eleventh AH due to the presence of prestigious Islamic mathematicians as well as glorious Islamic architecture from a geometrically known point of view. The study of analysis on manuscripts is very valid in scientific centers. These manuscripts have been analyzed by architecture in the form of face-to-face research and academic communication in the preparation of scanned images. The manuscripts belong to Islamic scholars including Buzjani, Farabi, Ibn Sina, Akhavan al-Safa, and Jamshid Kashani. In order to study geometry in the theories of Islamic mathematicians and to obtain basic information about geometry and mathematics, the deductive method has been used in research, and the contextualist approach has been used in the discussion of historical issues of architecture and knowledge topics of geometry. The research findings show the decision of Islamic mathematicians based on the issues of Islamic belief and thought to meet the practical needs in Islamic society and beyond. Islamic architects are also among the most important learners in the field of building architecture and related matters in terms of geometry. These topics are in the form of converting numerical mathematics into theoretical geometry in its quantitative and qualitative dimensions and practical geometry to achieve practical cases in providing applied geometry for educating architects. These teachings, due to their complexity and the fact that they belong to the mathematical field of equivalence, required face-to-face educational communication. This issue is called the meetings of artists between Islamic mathematicians and architects according to its own process.
In order to understand the knowledge of geometry by architectural experts in the period from the fourth to the eleventh AH, a subject has been created by Islamic mathematicians of that time that may have existed in previous centuries. This is the subject of communication classes created by Islamic mathematicians.
They tried to improve jobs in various fields. In the field of architects, this issue is called Artistics Meeting. Meetings in which Islamic mathematicians, with their vast knowledge and perception, have applied theoretical knowledge to the profession and minds of artists. The method of calculating geometry