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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So far, many scholars have spoken of mathematical and architectural mergers. Different perspectives in this regard suggest that there are two general approaches paraphrastic and historians in most of these studies. But what has not been said about this aspect is common mental practices in mathematical science and architecture knowledge that affects the work of mathematicians and past architects. Therefore, one can ask the question that «the presence and continuity of mathematics in the past architecture is due to the mental state of the architects?» The approach of the present article is based on the historical interpretation of documentary evidence, which, in the form of past texts and science databases, Investigates a procedure in the relation between the science of «mathematics» and the «architecture», in order to explain the mental structures among the activists of the two domains by examining the mathematical meaning of the past in the sciences on the one hand and the position of architectural knowledge with the predecessors of the other. The results of the research show that a special procedure of mathematics called the «algorithm» can be identified, which has been the cause of the mathematicians of the past, and has led to the birth of «cultural mathematics» in this context.

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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