جستجوی مقالات مرتبط با کلیدواژه « گره چینی » در نشریات گروه « هنر و معماری »

Masouleh is one of the few historical and habitable spaces in Iran, where the continuity of Iranian Islamic arts has been common for many centuries. Masouleh is located in the mountainous part of Fuman city with a thousand year old history. This historical city was registered as a national monument in 1944 and is currently being registered in the UNESCO World Organization. Masouleh’s architecture has a stepped structure and the houses are extroverted. Masouleh has six neighborhoods, Reyhane-bar, Asad-mohalleh, Keshe-sar, Khanebar, Masjed-bar and Bazaar. Reyhane-bar neighborhood is the main entrance to Masouleh and is located in the southern part of the city. The formation of Reyhane-bar neighborhood and its buildings is deep-rooted in the Zandiyeh- Pahlavi period. Reyhane-bar neighborhood has 50 residential units, of which 26 buildings have a historical structure and were examined in the current research. The Reyhane-bar neighborhood has a variety of latticed openings made of enclosing decorative patterns. The aim of the research is to recognize the types of openings and ornamentations in the Reyhane-bar neighborhood. The research questions are as follows: 1- In how many levels are the openings of the historical building of Reyhane-bar neighborhood classified? 2- What decorative patterns are used in the openings and what is the frequency of new to old patterns in the ornamentation of the openings of Reyhane-bar neighborhood? The research method is descriptive-analytical and the information collection method is documentary and field study. The results of the research show that the ornamentations of the openings of Reyhane-bar neighborhood have been implemented using three methods Girih-tiling, Ghavarehbori and woodcarving. The openings of the Reyhane-bar neighborhood are classified in six levels: integrated openings, without Sarbarieh (opening above the window), inscribed openings without Sarbarieh, Sarbariehs without a border design (single), and inscribed Sarbariehs (single) and Orosi. This should also be noted that the Reyhane-bar neighborhood has the lowest number of Orosis in comparison with other neighborhoods and Orosis in the above-mentioned neighborhood are mainly observed in the economic constructions. A total of fifteen decorative patterns have been used in the openings of Reyhane-bar neighborhood, among which, 8-square Shamse girih patterns and Paisley Ghavarehbori are the most repeated patterns. Reyhane-bar neighborhood has 6 new patterns and 9 common (original) patterns in Masouleh. The results of the research show that 24% of the decorative arrays of the openings of the Reyhane-bar neighborhood was of new patterns and 76% of the original and common patterns in Masouleh neighborhoods. A noteworthy point in the construction of the ornamentation of the openings of the Reyhane-bar neighborhood is the common use of the Ghavarehbori method. Among the main reasons for the Ghavarehbori construction method in the decorations of the openings of the Reyhane-bar neighborhood, the following can be mentioned: Cost-effectiveness: The Ghavarehbori construction method is much more economical than the Girih-tiling method, but by implementing Ghavarehbori, more limited designs can be made in comparison with the Girih-tiling method. Ease of construction: Artists need to use soft wood to make Ghavarehbori ornamentations, and this causes less durability, more wear and tear, and a more unfavorable appearance in the building wall. For this reason, to solve the problems of corrosion and to prevent biological and environmental disintegration as well as turbidity of color, the residents are forced to use stabilizers and chemical colors that do not match the authentic and historical texture of Masouleh. The research results show that there are sixteen geometrical patterns in Reyhane-bar neighborhood. As already mentioned in the text, the ornamentations of Masouleh’s openings have been implemented in three forms: Girih-tiling, Ghavarehbori and woodcarving. Several researches have been recently conducted with regard to the subject of Masouleh, its neighborhoods, and the existing ornamentations of the openings of each of these neighborhoods due to the significance and importance of Masouleh, as one the few habitable historical places in Iran. This research and its results are only a small part of the wide and extensive topics that can be performed in the field of knowledge of traditional arts and how they work to meet the needs of users. In fact, it is possible to investigate the ornamentations of other places in Masouleh in future research, which would lead to the recognition and preservation of the architectural arrays of Masouleh.

Decorations, as important components, have long been one of and the most stable characteristics of Islamic architecture and art. One type of these decorations is openings. In addition to practical aspects, openings have presented diversity and enclosing beauty in Iranian architecture. The surface of the openings has mostly been decorated with geometric and vegetal patterns. The city of Masouleh has various geometric openings that have been embedded in this city for many centuries. Masouleh is located near (55 km away from) Rasht in Gilan province and in the southwest of Foman in a mountainous area with a height of 1050 meters above the sea level. This city is registered in the list of national monuments under number 1090. In the present research, an attempt has been made to analyze the types of decorations in the openings, the abundance of decorations in each of the openings, the concepts of decorations, and the drawing of arrays in Masjedbar openings.

The current research aims to answer these questions: how many levels do the openings of Masjedbar neighborhood include? What concepts have been effective in the formation of arrays of openings in Masjedbar? In this research, an attempt has been made to analyze the decorations of the openings of 26 buildings in Masjedbar neighborhood, which are older than other residential buildings in this neighborhood. The method is descriptive-analytical and comparative. In the first step, the pictures of openings were prepared based on field surveys. In the next step, they were drawn by AutoCAD 2023 software. Also, to understand the proper amount of lighting, the dimensions of the openings, and the influence of the arrays on the lighting, optical simulation software "VELUX Daylight Visualizer 3" was used. In the last step, the results of the types of decorations in the openings, the abundance of decorations in each, the concepts of decorations, and the drawing method of the arrays in Masjedbar openings were presented.

The architecture of Masouleh has attracted the attention of many domestic and foreign tourists and researchers due to the use of authentic Iranian Islamic arts and its great compatibility with the nature and culture of society. The openings of the historical city of Masouleh, especially Masjedbar neighborhood, are one of the oldest and most beautiful arts where one can see the originality and artistic creativity of the artists of Masouleh and the province. Masjedbar neighborhood in Masouleh is considered one of the centers of the early formation of Masouleh; because of the presence of the mausoleum of Awn ibn Ali, it has earned special sanctity among the habitat of Masouleh. To meet the needs of its users, Masouleh’s buildings have various types of integrated openings, Sarbariahs with inscriptions (single), Sarbariahs without border design (single), openings without Sarbariah, and Orosies. The openings often consist of Girih-tiling and Ghavarebori decorations. Masouleh integrated openings have a two-part structure Sarbariah and bariah. These types of openings are the most common types of windows in Masjedbar neighborhood. The upper opening of the window, which is called Sarbariah, is fixed, and the bariah part consists of two parts that can be separated from each other. Sarbariahs are inscribed (single), have minimal decorations, and possess a minimum amount of space for light and ventilation. In the opening part of the bariah, a door without decorations is used, and the Sarbariah has two parts of girih-tiling decorations on the border and the middle inscription. Sarbariahs do not have a border design (single), have a similar structural and function similar to the windows of inscribed Sarbariahs (single) of Masjedbar neighborhood. Openings without Sarbariah in Masjedbar neighborhood have a surface with full light absorption capability in the bariah section and do not have Sarbariah or upper opening. The Orosies or rising windows of Masjedbar neighborhood have a structure with many Girih-tiling and Ghavarebori decorations. From the point of view of receiving light and natural ventilation of the interior, the Orosies are of a higher level than all other Masjedbar openings and have been used in the residential buildings and mosques of this neighborhood. The Orosies of residential houses have more decorations compared to the Orosies of mosques in Masjedbar neighborhood.

The research results show that Masjedbar openings are classified into five levels of integrated windows, openings without Sarbariah, Sarbariahs without inscriptions, Sarbariahs with inscriptions and Orosies. The present research results show that 19 geometric arrays of Girih-tiling and Ghavarebori were used in the structure of openings in Masjedbar. Ghavarebori arrays with checkered design, an eight-square shamseh knot, and a four-square knot are the most frequent patterns in the openings of Masjedbar neighborhood. The results of natural light reception analysis show that integrated openings, without Sarbariah and Orosies have a good performance in receiving light; Sarbariahs with inscriptions (single) and Sarbariahs without border design (single) have poor performance in absorbing natural light in Masjedbar neighborhood. The results of investigating the shapes of the geometric arrays of Masjedbar openings show that the plant shapes in the arrays of the openings are often taken from the designs and patterns of flowers and historical and mythological plants of Iran, which were very common in Iran's pre-Islamic buildings. Cypress tree, paisley, and lotus motifs are included in this category. Religious and cultural motifs and symbols are other effective factors in the formation of arrays of Masjedbar openings. Ghavarebori, chalipah, and chaharqol are more widely used in the openings of Masjedbar's religious buildings. The rhombus square knot is one of the few patterns native to Gilan in the arrays of Masjedbar openings. This pattern is often used in the openings of residential buildings and is a symbol of mat weaving in the plains of Gilan. The combination of numbers and basic geometric shapes is another effective concept on the formation of arrays of Masjedbar openings. These shapes, involving a combination of number eight, four and circular, rectangular and square motifs, are among the most used patterns in Masjedbar’s opening arrays.

The dynamic relationship between culture and art influences both domains significantly. Within various cultures, the adoption of decorative patterns holds particular significance. The selection and evolution of decorative patterns are influenced by each culture's context. Historical artifacts reveal that geometric decorations have long played a central role in human culture, undergoing progressive development over time. A subfield of geometry known as "Girehes" has extensively permeated Iranian-Islamic architecture, directly influencing its aesthetic foundation. The realm of Girehes intertwines mathematics and aesthetics, originating from a context of robust mathematical inquiry. Although historical records are scarce, they suggest that adept practitioners of practical geometry orchestrated the design of Girehes found on historical monuments. However, these designers rarely sought to establish a purely mathematical or theoretical basis for their designs.Gireh's principles, rooted in mathematical foundations, have captivated contemporary researchers worldwide, owing to their mathematical underpinnings. Surprisingly, adherence to geometric and mathematical principles has not stifled the diversity within design and structure. On the contrary, artists during the Islamic era expanded the scope of geometric patterns with remarkable diversity. Notably, one prominent classification system within Girehes revolves around their respective families. This taxonomy encompasses Acute, Median, Obtuse, and Two-point categories, based on the angle formed by the lines of the "Shamseh," a central motif that reverberates across the entire Gireh design.However, it's noteworthy that not all Girehes adhere to a specific angle formed by the Shamseh lines. Nevertheless, a substantial majority of researchers tend to rely on a categorization hinging on angles of 36 degrees (Acute), 72 degrees (Median), 108 degrees (Obtuse), and Two-point, due to their prevalence. It's essential to recognize that the angles attributed to Gireh families are not universally applicable. Variations include Girehes featuring angles of 30°, 60°, 90°, and Two-point, or angles of 45°, 90°, 135°, and Two-point.To address questions surrounding the diverse angles between star lines leading to Gireh classification into various pattern families and the structural rationale behind the modular arrangement of angles within these families, this study employs a descriptive-analytical approach. It leverages library resources to delve into the structure of six-, eight-, ten-, and twelve-point Girehes, aiming to unveil the geometric underpinnings of Gireh families and the correlation between angles in different families and the Girehes' structures.Girehes, part of the Islamic artistic tradition, comprise tessellations formed by regular geometric shapes harmoniously arranged to maintain uniformity. Known as "Gireh-Work," this form of geometric decoration often juxtaposes the "Shamseh" motif with polygonal elements to create a balanced composition. Traditional masters and modern research corroborate the notion that Gireh hinges upon a harmonious interplay of components. This interplay, however, is not arbitrary; beneath the Gireh motifs lies a concealed layer, termed the "underlying generative tessellation," elucidating the overall order of Gireh compositions. This generative tessellation forms the basis for drawing Girehes, allowing the placement of various Gireh motifs. Given Shamseh's critical role, artists and masters assign diverse names to it based on the number of Shamseh points. This motif profoundly impacts the overall design, shaping its structure. The foundational stars of Gireh often stem from this process, frequently defined by the connection of midpoints in the underlying polygons, which in turn determines pattern lines.Shamseh's significance extends beyond the individual motif to dictate the broader Gireh structure symbolically. Consequently, the angle of the Shamseh influences all Gireh motifs and determines their respective families. Three main categories of classification emerge based on the points' arrangement, encompassing eight-pointed, six- or twelve-pointed, and ten-pointed Girehes. Classification by Shamseh angles yields four categories: Acute, Median, Obtuse, and Two-point. In earlier times, artists relied on drawing rules grounded in circle divisions, lacking modern tools to measure line angles accurately. Consequently, Gireh angles were often determined through methods aligned with the number of Shamseh feathers or multiples thereof.The connection between Shamseh points and Gireh's structure is profound; assuming a Shamseh point count corresponds to a radial division of the circle, the number of Shamseh points shapes the angle structure of the entire pattern family. With α and β representing the angles of Shamseh lines, and P denoting the number of divisions in the pattern family, while F signifies the division number modulus in the Gireh family, the relationship can be expressed as follows:α = β = F/P × 360° = A°This circle division modulation closely corresponds with the fundamental polygons of Girehs. Classification of Gireh families rests on the base polygon, relying on connections of line segments between points on the polygon's sides. Regular polygons can be circumscribed within a circle, aligning the modularization of node families with radial divisions. This arrangement is evident in six-, eight-, ten-, and twelve-point Girehs. If the modularization equals the distance of one unit from the middle points in the base polygon, it's classified as Acute. Similarly, if the distance equals two units, it's Median. For a three-unit gap, it's considered Obtuse. Finally, the placement of Gireh lines at 1/4 of the polygon's sides or vertices, instead of the middle point, signifies the Two-point family.Evidence of Gireh's historical reliance on polygon techniques is further demonstrated by the alignment of angles in Gireh families with the angles formed by lines at the polygons' midpoints. Gireh designers effectively harnessed polygons' geometric structure to craft intricate Gireh patterns within an encompassing framework known as the underlying generative tessellation. The division of the circle directly corresponds to the base polygon's grid system. The number of fold divisions dictates the base polygon's sides – a 12-fold division corresponds to a dodecagon, a 10-fold division to a decagon, and an 8-fold division to an octagon. Acute, Median, and Obtuse families are harmoniously woven using lines connecting midpoints in the primary polygon through a generative tessellation. Correspondingly, the Two-point family neatly aligns with the polygonal structure, deviating from the middle point to formulate patterns based on distances from middle points to vertices.

Knotting is one of the most regular geometric decorations that spread with the spread of Islam. Among the different Islamic governments, the Ilkhani era is one of the most brilliant periods of prosperity and flourishing of art and architecture with the use of knot-making in Iran. Among the magnificent buildings of this period are Kabud Dome and Ghaffarieh Dome, located in Maragheh city, the external surfaces of these buildings have knots with different characteristics and many knot tools that are creatively used in each one. The purpose of this research is to know the types of knots, and analyze their characteristics and characteristics; It is the use of knot tools in these buildings and the comparison and matching between them that reveals their differences and commonalities. The current research aims to answer these questions: "What are the types of knots and the position of the knots on the external surfaces of the Kabud Dome and the Ghaffarieh Dome? And what are their commonalities and differences from each other?" The upcoming article is done in a descriptive-comparative way and the information is a combination of library sources and field observations. The results show: even though both buildings belong to the same period; two types of knotting with two different implementations have been used in both buildings. In this way, Ghaffarieh Dome's tilework is made with a combination of brick and mosaic tiles in a semi-relief form, and the nodes are used separately with mosaic tiles in the moqrans, But the knots of the Kabud dome are all made with cut bricks of almost the same size in a mosaic style and all raised; Also, most of the node tools do not have separate uses.

Decorative arts had emerged in various forms in the Islamic world, and Gireh is one of the most complex forms that constitute an essential part of the Islamic arts in the world, which had developed over time. These rely on the geometric rules in the mathematical sciences. One of the most critical issues in the studies of Gireh is the methodology knowledge of their designing and drawing that different researchers emphasize on different methods. Knowledge of the design methodology of Gireh is closely related to its aesthetics and originality. Iranian Islamic architecture significantly contributed to the development of Girehes, but their connection with their methodological knowledge was not obvious. Many scholars consider the method of developing Gireh in Iran based on the radial (Falaki) method, which has remained in the written sources of the last traditional Master of Iran. However, studies on historical documents such as the Topkapi scroll and the Girehs that remained on the Gonbad Soltanieh show that Iranian architects and artists were fully aware of the polygonal method and Gireh production techniques based on it and it used for developing Girehes in Iranian architecture. Therefore, this research seeks to answer the following questions with descriptive-analytical and reasoning methods by collecting information through libraries and field studies: 1- What evidences are left from the past that shows the use of polygonal technique to produce Girehes? 2- How had the application Process of the polygonal technique to the development of Girehes in Iranian architecture? 3- Why did the Iranian Master introduce the radial (Falaki) method to drawing in their books despite the polygonal technique? To answer these questions, after introducing the methodologies of Girehs production, the structure of Gireh is examined from the polygonal technique point of view along with its historical documents. Then, the developing process of Girehs in Iranian architecture is studied based on the development of underlying generative Tessellation. Finally, the radial and polygonal methods are compared, and Their application among the traditional Masters of Iran is examined. Despite numerous studies on the development of Girehs and polygonal technique, the new achievements of this research is new evidence of Girehs left on the surfaces of historic buildings, which presents the application of the polygonal technique in Iranian architecture. These expand the methods of using the polygonal technique to develop Girehs in Iranian architecture. These documents also show a new path in the development of Iranian Girehs, which indicates the use of the Gireh as an underlying tessellation in producing more complex Gireh such as Pili and dual-level Girehes, which is investigated in this study.The Knowledge of Girehes designing and implementation was a family knowledge and available to certain people in the community that architects passed these methods from one generation to the next generation in a secure way to prevent the revealing of this knowledge and usually transfer permission of this knowledge didn’t happen easily. Despite these limitations, methods of designing and applying Girehs were developed in various branches. Although the methods of producing Girehs are extensive and varied, some artists even invented their drawing methods. The four methods are prevalent among designers and researchers of this art and are widely used, including Radial (Falaki), Point-Jointed (Moroccan), the Grid, and the polygonal techniques. The polygonal method is the subject of this research discovered by Ernest Hanbury Hankin when he was visiting an Indian bath and was introduced to the contemporary world. Later, researchers realized that this method is historical by studying historical documents such as the Topkapi scroll. This method is often determined by drawing lines that connect from midpoints to each other’s in the underlying main polygon to create the main stars and the application of pattern lines. The presented method approximately adheres to J. Lee Registration, which creates a given star by identifying the number of sides of the main polygon relative to the number of consecutive sides at the midpoint to the midpoint of the line.Suppose the development Process of Girehs in the Islamic architecture of Iran is examined. In that case, it can be seen that the historical development Process of Girehs began with the formation of patterns on an orthogonal Grid and ended with a very complex tessellation. In addition to observing this method in the Topkapi scroll, the application of this method in the tiling of Gonbad Soltanieh is also evident; the designer kept the underlying generative tessellation in the final design. In addition, the same underlying generative tessellation was used to create another Gireh. Instead of arranging the Alāt (motif) at the midpoint, the Gireh was arranged according to the vertices of the underlying tessellation. It caused three Alāts of Shāmseh to meet at one point. Despite contemporary researchers emphasizing the midpoints of polygons in underlying tessellation in applying the polygonal technique. In addition, the use of Gireh as underlying generative tessellations is also evident in this building to produce Girehs, due to which the next generation of Gireh such as Pili Gireh was created in the Yazd Grand Mosque. In these Girehs, the Alāts of underlying generative Gireh were interweaved by Alāts. Due to this, the number of hidden layers increased. Because in addition to the generative Gireh (underlying tessellation of pili Gireh), there is also another underlying tessellation for the generative Gireh. The last stage of Gireh development is the dual-level Gireh (Shah-Gireh), which uses one Gireh as the preliminary design for the secondary Gireh inside the Alāts of primary Gireh. It is impossible to achieve such a design by using the radial method or applying the symmetry of a fragmented Alāts of Gireh. However, the polygons must be manipulated in the underlying tessellation, which shows the application of the polygonal technique in the history of Gireh development. The polygonal technique is evident from the existence of polygonal tessellation in the Topkapi scroll and Girehs on the remained surfaces of the monument and considering that in the evolution of Gireh in Iranian architecture. The main problem of the radial method is the impossibility to design a new Gireh, the whole process of drawing a Gireh in the radial method is step by step, and the artist needs to follow all the steps, the way of determining the secret line Also is not clear in this method which other arcs are defined. This line in the drawing of the written sources of the masters shows predetermined. In contrast, the polygon method is based on the combination of underlying polygons. Understanding this process makes it possible to place motifs in tessellation, draw the Gireh shape without following a special process, and change the tools based on the underlying tessellation. He came up with various designs. As well ass, it reached various designs by changing motifs based on tessellation. According to the study, the application of the radial method can be for implementing the Gireh on different bases that work be easier based on the tools of architects and artists of the classic era and prevented the disclosure of the design method of Gireh.

Islamic geometric arrays is among the most clear declaration of geometry and mathematics in all kinds of Islamic art including wooden, metallic, painting arts and in utmost architecture as well as Islamic artists and artisans have extensively utilized it in the production of their works. The geographical broadness utilization of these arrays covers the three continents of Asia, Europe and Africa, and in timeliness, simple geometric arrays are evident from the beginning of Islam in the Umayyad palaces up to now which its complex types are plenty found. Scholars have excavated Samarra to prove that the origin of the third/ninth century decorations of the Ibn Tulun Mosque in Cairo was Baghdad during the Abbasid period; On the other hand, the early Islamic architecture of Khurasan and eastern Persia establishes the Samanids, Qarakhanids, Ghaznavids, Ghurids and Seljuks as principle contributors in the maturation of the geometric ornamental tradition. The collective architectural legacy of these cultures reveals the significance of their contribution to our knowledge of Islamic geometric design. According to what has been mentioned, the origin of the methods of drawing Islamic geometric patterns and their differences and similarities can be an arena for explaining, classifying and characterizing the drawing of those patterns. The surviving works, in which the geometry of complex Islamic motifs are used, are available from the early Islamic centuries, but it seems difficult to identify the precedence and lag of the methods of drawing them. Assuming that the method of drawing these designs is very diverse among artists from different regions, the present article seeks to study the similarities and differences between the two regions of Asia (Iran) and North Africa (Morocco). Since in both regions the methods of drawing and execution are usually quoted in the manner of oral speech and can be forgotten. Also, the familiarity of artists and artisans with the methods of drawing patterns in non-native areas can create a change in the production of works of art. It is necessary to conduct research to explain the characteristics of drawing Islamic geometric patterns in both regions; therefore, this article, while explaining the method of drawing Islamic geometric patterns "Hasba" (derived from Arabic word: Hasaba, which means: calculating) is common among Moroccan artisans and the Iranian method, it also seeks to examine the differences and similarities, advantages and disadvantages of each of those methods. The main question is how to analyze the similarities and differences between the theoretical geometry of these two methods using a comparative research method. The method of collecting library information and redesigning the projects has been done by Corel Draw software. The statistical population is 15 Iranian Islamic geometric patterns. The sampling method is selective and in order to refute and confirm the problem, feasibility study, explanation of differences and similarities have been selected. The method of data analysis is visual comparison. Moroccan artisans have strict rules for drawing geometric patterns, based on "Laqtib" equivalent to "Hamil" in the Iranian style, which consists of thin strips that form geometric motifs, and throughout the design, they are tufted and crossed one after the other. The width factor of these strips forms the main background or frame in this method. Also four times the width of the Qassama, they form "Zaqaq" (in Arabic literature: narrow alley). At the four corners and halves of the Zaqaqs, concentric circles are drawn, from the center of which and their tangential points, guidelines are drawn to adjacent circles, which are the primary role of Moroccan geometric patterns. Then, in the circle, the pattern of Mohr Soleiman (Shamseh Shesh) is drawn and along its sides, the rest of the geometric patterns are formed in order. But the theoretical method of drawing geometric patterns among Iranians is known as the radial method, which dates back to at least the fifth century AH, which is the basis of many contemporary writings in this field. In the radial method, the width of the doorway is the basis of the drawing, and usually the length of the background rectangle is determined by dividing the angles into several equal parts and drawing the radii and guidelines. As in the method of Hasba, in this method, a sun motif is placed in one of the corners, and along the sides of that sun, the rest of the motifs are determined. In this article, while introducing both "Hasba" and "Iranian" radial methods, the method and analysis of the similarities and differences between the theoretical geometry of these two methods are explained using descriptive, analytical, and comparative research methods. The main question is how to analyze the similarities and differences between the theoretical geometry of these two methods using a comparative research method based. Finally, the feasibility of drawing fifteen Islamic Geometric Designs ("Dah-Kond", "hasht-Zohreh" in Farsi & etc.) in both "Hasba" and Iranian methods will be investigated comparatively. The result of this research shows that in both methods, the framework is an important and one of the basic elements of drawing. The frame is only square in the Hasba method with the initial proportions, and if it is in the rectangle, it is a repetition of the primary square pattern with a ratio of one to two (Today's researchers have been able to execute it in regular polygons by rotating lattice designs), and in the radial method, this ratio is approximately 1.137 in " Dah-Kond" (the name of Geometric Designs in Farsi), which is closer to the golden rectangle and visual aesthetics. The Hasba method is calculated according to the following pattern with a special rule and a coefficient of the thickness of the Laqtib. Laqtibs sometimes make small patterns impossible, but in Iranian examples, the Hamil is determined according to the needs of all kinds of applied arts, after drawing the knot. In Hesba, the Mohr Soleiman is certain, but the motifs between the suns are unknown and can be variable, while in the Iranian example, the task of all the motifs is determined from the very beginning; the variety of motifs in the radial method is greater than in Morocco; Hasba sub-patterns variety cause other motifs, but can cause confusion and error for the master. The "Shamseh" or the Mohr Soleiman motif is one of the main motifs of Islamic Geometric Designs in both methods. The area of the "Hesar" in Hasba has the status of a border, which does not exist in the Iranian example compared to Hasba, but can be added. Finally, the drawing of many Iranian Geometric Designs, including the case example of "Ten Kond Geometric Designs" cannot be drawn by the method of Hasba. Indeed many Iranian radial knots cannot be plotted by the Hasba method due to the mismatch of length and width ratios as well as matching angles with a multiple of 18 and others. But some simple, such as "Eight and Venus" & "Moje-Asiyabi" & "Chahar Sekeron" & "Hasht-Seli shakhakdar", can be drawn with the Hasba method. The Hesar area may be considered as one of the advantages of the "Hasba" method, which can be drawn but does not exist in the Iranian method.

The art of Girih tiling is a collection of geometric shapes that are placed next to each other in a harmonious order. The city of Masouleh is one of the historical structures in Guilan province, which includes many decorative arrays used in the construction of openings. The purpose of this research is to recognize the decorative types used in the openings of Asad-Mahaleh of Masouleh. The research method is descriptive-analytical and the library method was used to identify the decorative types used in the openings. The research questions are as follows: In how many levels are the openings of Asad-Mahaleh building classified? What Girih tiling and Ghavarebari patterns have been used in the openings of Asad-Mahaleh Buildings? The results of the research show that the decorative arrays of the openings of Asad-Mahaleh buildings are classified in three levels: integrated windows, Sarbariah openings with inscriptions and Sarbariah openings without a border (single). The decorative arrays of the openings of Asad-Mahaleh consist of fifteen patterns of Girih tiling and Ghavarebari. Eight-square Shamseh Girih patterns and Ghavarebari with Paisley design are the most repeated patterns in the arrays of Asad-Mahaleh openings. Also, the results show that Sarbariah with inscriptions and integrated windows have the highest pattern of Girih tiling and Ghavarebari, and Sarbariah without a border design (single) have the least pattern of Girih tiling and Ghavarebari in the openings of residential buildings in Asad-Mahaleh of Masouleh.

The diversity of Girih tiles has led to their wide usage in architecture. Khansar and Golpayegan are located on the margin of Dasht-e Kavir with religious, residential, and service buildings. Girih tiles play a crucial role in architecture of above-mentioned cities. The purpose of this study is to recognize and understand the typology of the technical and artistic characteristics of Girih tiles in the buildings of Khansar and Golpayegan. The present study seeks to discover the different Girih tile techniques used in the religious and non-religious building of Khansar and Golpayegan. This research also deals with the different typology patterns and form of Girih tiles in aforementioned buildings. The research method is descriptive-analytical and the sampling method is targeted convenience. The data collection was in the library and field study forms. The results show that Girih tiles were used in sash windows, normal windows, main doors, openings, tombstones, Minbars, and Zarihs in religious buildings of Khansar and Golpayegan, while they were utilized the windows, openings, and sash windows in non-religious buildings. The Girih tiles of religious buildings have a wider application. "Hollow Linework" was the most common technique. The linework and glass were mostly used for creating sash windows and slating, while the linework and different textured Girihs were used more in religious buildings than non-religious ones for creating entrances. Different geometric Girihs can be observed in religious and non-religious buildings of these cities, but the religious buildings have more diversity. Four, six, eight, ten, and twelve Girihs are regarded as the most common and the four based Girihs have the widest application.

Two methods, periodic or quasi-periodic, are used to cover surfaces with geometric shapes. In the periodic method, the unit of repetition is based on transitional symmetry; But the quasi-periodic method lacks transitional symmetry and is much more complex than the periodic method. Quasi-periodic order is also one of the micro-scale arrangements found in natural materials. Quasi -crystals -materials of this order that were discovered in the late twentieth century- exhibit a special symmetry and violate the rules of conventional crystallography, which are based on transitional symmetry. Recent research in this field shows that Iranian architects have long been familiar with the quasi-periodic order. The use of this order has so far been proven in the decoration of three historical monuments of Iran, the oldest of which is the Gonbad-e-kabood of Maragheh and belongs to the late sixth century AH (late Seljuk era (Seljuks of Iraq)). The main question of the research is whether there is another (older) building in Iran that has decorations with a quasi-periodic order? This article, with the hypothesis that Iranian architects have been familiar with this particular geometric order at least since the early Seljuk period, aims to study the knotted decorations of the Taj al-Molk dome (481 AH), which is one of the most important buildings of this era. Is, put. Research method This article is based on descriptive-analytical research method and logical reasoning; according to which, the geometric infrastructure network in the knotted decorations of the previously studied buildings has been compared and has become the basis for achieving new results in this research. Comparing the order in the designs of Taj Al-Molk dome with the structure of quasi-crystals, it was found that at least one of its internal nodes has an arrangement with a quasi-periodic order (of the seventh-degree rotational symmetry type). Thus, this is the oldest architectural example of the art of geometry with quasi-periodic order in Iran, which has been identified and introduced so far, and the use of quasi-periodic order in Iranian architecture dates back to the late fifth century AH.

One of the traditional arts related to architecture is Girih wood working which is used in different spaces based on structure and components, and therefore has an effective role in the richness of the architectural space. The purpose of this study is a comparative study of visual features and decorative patterns of Girih wood workings in traditional architecture of historic residential houses. The historical period of these works includes the Afshar, Qajar, and early Pahlavi periods, all of which are located in the city of Darmiyan in the province of South Khorasan. The present article is descriptive-analytical in terms of attitude and approach to the problem and content analysis in terms of method. In this study, 5 historical houses including Tavakoli , Abdul Azim Beyk , Abdullah Beyk, Abdullah Khan and Mahdi Khan Houses which possess wooden Girih decorations have been studied . The results of this study show that most of the girih are of mesh type and the least number are of solid type. The most diverse girih can be seen in the house of Mehdi Khan Rafiei. The most common application of girih in the residential architecture of the studied houses is the use of mesh girih in the openings (windows). This type of girih , in addition to providing light and maintaining wind flow, has maintained the privacy of the private space due to its use in the summer living space on the upper floor of the mansion. In terms of matching the quantity and quality of girih works with the historical period of each building, it can be said that the more historical the houses are, the more variety and quality of works there is in residential architecture. Therefore, in the houses belonging to the late Afshar dynasty, such as the house of Abdullah Beyk and the house of Mehdi Khan Rafiei, the art of girih has been used more widely than the houses of Qajar (Abdul Azim Bayk) and Pahlavi (Tavakoli). The research data indicate that at least 11 different types of girih can be identified in the studied houses. The most prolific and diverse geometry of the designs can be seen in the construction of Tavakoli and Mahdi Khan Rafiei Houses. In addition, the most widely used geometry is girih naming "eight and four". According to the results of the present study, Mehdi Khan Rafiei house has the most diverse type of girih making both in terms of geometry of designs and in terms of application and use of girih in interior architecture.

Gerehchini (latticework) is one of the most prominent patterns used in Iranian handicrafts and buildings. It should not be considered as a mere visual pattern, but in principle as a solution to solve executive challenges. Carpentry latticework is a type of geometrical pattern used in making fences, doors and most of all latticed windows. Due to the vulnerability of wood material, especially owing to its proximity to the open air, as serious study of such structures have to be carried out. An analysis of latticework and the tradition of making such works can now be done by present masters and the few images and examples remained from the traditional Iranian architecture. In this article, an attempt is made to explain the strategic reasons for using this type of pattern by examining the various aspects of the factors affecting the formation of this type of lattice.The purpose of this study is to identify the factors affecting the carpentry latticework used in latticed windows and to explain the reasons for the difference between such a lattice and other related types. Defining the nature of carpentry latticework depends upon understanding the way it is made. The function of windows, features of wooden constructions and construction methods, basic knowledge of flat geometry, visual aesthetic development of artists and architects are among the factors influencing the formation of carpentry knots. Reviewing these cases by field and library studies with a descriptive-analytical and modeling approach, this article is done with the purpose of having an accurate representation of the carpentry latticework and making an analysis of the feature of this type of lattice. One of the results of this research explains three factors, i.e. function, appearance and technology in the formation of the mentioned lattice. Incidentally, the role of different factors in the formation of this type of lattice is examined by looking through a detailed study of its construction.

Knotting designs ornaments and geometric patterns in Islamic art have many common features. Perfection and implementation of knotting designs ornaments and the use of geometric patterns in Islamic Iran both refer to the Seljuk period. Qajar-era Chinese knot ornaments and geometric patterns had many ups and downs connected with the arrival of wild-Maby. During that period Iranian culture was undergoing many changes. Masr Qajar art and architecture of Iran with the exception of a few examples stopped being connected with the government. The most brilliant examples of the Qajar architecture are palace-fortress in Chaharmahal and Bakhtiari Province Chaleshtori (Dezzak Castle). Under their arches, there are beautiful examples of Knotting designs with geometric motifs made of wood, metal and mirrors. Local influence on these samples is obvious. In this regard we can see dramatically more complicated and elegant interior designs and decorations on the top of porch roof. The major reason is that the maintenance of the interior to the exterior decorating easier. Iranian art has always created eternal beauties with thought and knowledge. Along with a beautiful understanding of mathematics and geometry, it has succeeded in creating geometric and decorative patterns such as porcelain knots. Chinese knot is an art from the Islamic era that has adorned magnificent and beautiful buildings from all over Iran and has given a valuable effect to the interior and exterior decoration of buildings, especially roofs and doors. This art can be seen in areas that have been safe from foreign invasion and have remained intact, such as Chaharmahal and Bakhtiari province. A beautiful art that has been able to impress Bakhtiari readers and the Lorish people and decorate their buildings and palaces is in this style. Extensive and relatively specialized research on cultural heritage and industrial arts in Chaharmahal and Bakhtiari province took a serious shape after the establishment of the Faculty of Arts at Shahrekord University. This article is the result of the recorded studies of the authors of this article and other researchers of the same faculty, which has formed the history of this research. Regarding the castle palaces of Chaharmahal and Bakhtiari province, studies have been done in relation to the field of architecture. Less attention in construction and architecture was paid to the industrial arts. Most of the studies in this regard were done by handicraft students of Shahrekord Universitychr('39')s Faculty of Arts in student dissertations, but recent example is new and unprecedented with the approach of paying attention to the geometric patterns in this castle palace. Geometric patterns, in addition to geometric beauties, refer to immaterial and metaphysical matters semantically and aesthetically. The spiritual and non-figurative nature of these motifs, which are mainly in terms of visual games, fluidity and mental movement and summative rotations and moving the corners and angles with special mathematical and geometric features, in terms of sensory visualization full of fit, rhythm, movement and dynamics. Most figurative motifs and images cannot have such an impact. In terms of visual autopsy, the adherence of geometric patterns to the geometric cryptic nature of the pure elements of nature, especially the strange overlaps of parts to whole and whole to parts and the fit of the original patterns with the developed patterns that play more like magic and also wonder at the numerical and quantitative proportions in The patterns, which are mostly naturalistic and interpreted only in a bit of mathematical language, speak to the beauty and astonishment of these hidden aspects of nature. They eventually manifest themselves in the form of geometric patterns. When a circle alone can create countless roles and nodes without computational tools and simply by repeating similar situations and spreading it to all points where it can be placed anywhere in the circle, and everything we see fits perfectly. This is nothing else but the embodiment of the hidden layers of nature. This concealment, which remains mysterious with the image of the image, as long as it sits on the body of man-made products, spreads the same mysteries and magic, and impresses the things (products) with the spirit contained in the roles.

From the past to the present, the historical villages of Masouleh and Abyaneh have had many similarities in the fields of decoration and architecture despite the climatic, geographical and ancient differences, and the existence of such commonalities has always been of interest to many researchers. Considering that the use of decorations such as gereh-chini is being forgotten in contemporary times and also no comprehensive research has been carried out on the gereh-chini structures of Masouleh and Abyaneh villages, the present study is trying to preserve and record such a valuable heritage. The authors use comparative studies to answer the following questions: Have the use of gereh-chini decorations been effective in creating architectural spaces and climatic adaptation of the two villages? What are the differences and similarities in the visual structure of gereh-chini and functional patterns of the windows of the two villages? The research is descriptive-analytical and comparative, and library and field research has been implemented. Also, in the climatic analysis of the samples, VELUX Daylight Visualizer 3 2019 architectural software has been used. The results show that gereh-chini decorations in both villages have created spaces such as ground floor entrance corridors, mashrabiyas, pre-entrances and in the window openings as small and large windows and railings, and in the construction of gereh-chini in the historical village of Abyaneh, more diverse materials such as bricks, clays and more native and original woods have been used compared to the historical village of Masouleh. The results of climate analysis in the software environment also show the appropriate functional effects of gereh-chini in light control and entrance in winter and summer in both villages. The results of the analyzes in the patterns section of the two villages also indicate that there are 18 gereh-chini patterns in Masouleh village and 8 gereh-chini patterns in Abyaneh village, of which 11% of the patterns in the two villages have structural and nominal similarities.

Sash windows are windows where the glazed panels are opened by sliding vertically with colored glasses that can pass sunlight with different colors in proportion to the hours and intensity of radiation. Masouleh historical city is one of the areas with the most remarkable sash windows in its architecture. In this research, it is tried to categorize various types of sash windows in Masouleh historical city. It is also tried to analyze and evaluate the visual, structural, functional and light features of sash window. The present research has used field method and descriptive-analytic studies to achieve these goals. The results of the research indicate that sash windows in Masouleh can be categorized in 6 different types of diverse sash windows, such as non-porous market sash windows, double glazed one-Daraki sash windows, two-Daraki sash windows, three-Daraki sash windows, four-Daraki sash windows, and five-Daraki sash windows. Also, by reviewing and analyzing the visual and structural features of Masouleh's sash window, the main reasons for the appearance of different types of sash windows are as follows: creating more human dimensions in the dimensions of the openings, creating a suitable covering (Hijab) for users in the interior, creating visual visibility proportional to user-friendly conditions (Animating), increasing physical protection from older users and children, reducing energy consumption, as well as weight reduction in buildings in order to reduce vulnerability to earthquakes.

Islamic art mostly avoids figurative images to avoid creating objects of worship. This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically-based decoration. Islamic patterns are created to lead the viewer to an understanding of the underlying reality, rather than being mere decorations, as writers interested only in pattern sometimes imply. In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul. These patterns in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6 to 13 point patterns by the 13th century, and finally to include also 14 and 16 point stars in the sixteenth century. So, many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate and complex patterns. In all of these patterns, circle has a very important role because the circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. Based on the shapes drawn from the circle, the earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all across the Islamic world. The next development, marking the middle stage of Islamic geometric pattern usage, was of 6 and 8 point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread. A wider variety of patterns were used from the 11th century. Abstract 6 and 8 point shapes appear in the Tower of Kharaqan at Qazvin, Persia in 1067, and the Al-Juyushi Mosque, Egypt in 1085, again becoming widespread from there, though 6 point patterns are rare in Turkey. In 1086, 7 and 10 point girih (knot) patterns (with heptagons, 5 and 6 pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10 point girih which became widespread in the Islamic world is the subject of this paper. Girihs are elaborate, interlacing patterns, formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. Girih designs are traditionally made in different media including cut brickwork, stucco, and mosaic faience tilework. In architecture, girih forms decorative interlaced strap work surfaces from the 15th century to the 20th century. Most designs are based on a partially hidden geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-, 4-, and 6-fold rotational symmetries which can fill the plane. The visible pattern superimposed on the grid is also geometric, with 6, 8, 10 and 12 pointed stars and a variety of convex polygons, joined by straps which typically seem to weave over and under each other. A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons. All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and thus suggest infinity. As it is cited above, in this article, the method of 10 point girih drawing is essayed and in order to maintain and ease the use of this lasting legacy in contemporary Iranian Islamic architecture, the question arises as to how to minimize the tools and stages of 10 point girih drawing, invent a method for drawing schematics in addition to speeding up the practice of drawing and applying the motifs. Authors, in response to this question, focusing on one type of girih (acute and obtuse 10 point girih), have developed a method called the Golden Star, which presented an original pattern for drawing shapes with a constant ratio in the resulting elements based on golden proportions and golden ratio. In this research, a combinative method has been used. The data collection is based on library research method and published documents, and a kind of logical methodology based on mathematical relationships and mathematical proportions is used for presenting a suitable model for drawing the 10 point girih. Therefore, in this paper a new method for 10 point girih drawing is presented.

Geometric designs (both normal and abnormal) and purely geometric interlaced patterns involve mental imaginary forms which are essentially superior to the perception- based naturalistic images. The patterns were not aimed to capture the reality perceived through the eyes, but they were supposed to create a glimpse of astonishing beauty in the artist’s creative mind or soul. Due to avoiding utilization of human figures and abstaining from idolatry, decorations have specific geometry in Islamic art and architecture. One of the striking characteristics of the knots (girih) that has caused to dynamicity throughout its thousand-year history is its regeneration and diversification of the diverse geometric properties. Girih tiles are used in Islamic art and architecture. Iranian Chinese Knotting is one of is one of traditional fields and professions that depends on geometrical patterns and on the first encounter, the spectator, is subconsciously affected by its discipline. Geometrical patterns, which are the source for the art Chinese Knotting, usually contain a polygon star in
the middle (the Shamseh) and some other geometrical figures so that they can cover the remaining space. Chinese knotting is not specifically a certain decoration or a means of conveying the emotions of the artist, but also the point of making them regarding to two ways: acting on the basis of their own knowledge and guiding others towards this knowledge. When a spectator looks upon the works of Chinese Knotting, they’re first affected by its beauty and especially its discipline, but after some more contemplation they are driven into the art’s mystical meanings. Girih tile is a part of Islamic architecture and art while its different types are used in the following arts: Wood carving, tiling, plaster, Khātam , brick work, mirror work, stone work and in carpentry as fences, door and window, wooden decorations and wood carving of Minbar and in blacksmith Iranian architecture. Girih tile is an intelligent interaction of aesthetics and function. Islamic artists have applied local materials in accordance to the functional requirements and cultural issues of each region. The valuable examples of this art are observed in historical city of Masoule located in the mountainous area of Masoule in Gilan (Iran). Wood is one of the highly applied materials in traditional architecture of Gilan with its different types. One of the greatest arts is seen in the historical city of Masoule with Girih tiles. Wood is used in this region due to its climatic condition and the need to a good thermal isolation against heat and cold weather. Also, wood is the first material being
applied in openings. Girih tiles decorations in this historical city are abundant in the buildings while their main façade is to the south. One of the advantages of using Girih tiles in openings of this historical city is to control the direct light in
different seasons of year. The aesthetic aspect is on the second priority. The beauty of Girih tiles, their coordination and part to total tendency in all openings have improved the unity and beauty of the historical buildings of Masoule. Sash window, other meshes and Telar with combination of decorative plants in the façade of buildings in Masoule have increased the aesthetics of this city. Historical city of Masoule is a good model for sustainable architecture and its final aim is respecting the culture and friendly relationship with nature and improving the life style of its residents. In the current study, the effort was concentrated on categorizing the designs (Chinese Knotting) used in the neighborhood of upper Kash-e Sar in Masouleh. The factors that affect the designs have also been inspected. The results show that 13 types of Chinese Knotting exist and that the most used pattern in this decorations is the pattern of eight-and-four. These results also show that the four fundamental parts of Chinese Knotting of Masouleh have been modeled on cultural,
religious and natural elements. The four common elements of the Chinese Knotting of Masouleh are as follows: The Shamseh (the sun), the eight leaved lotus (symbol of the circle of nature), Chalipa (the symbol of the four main elements, existence) and the circe (symbol of eternity, although in this particular design it is the symbol of trees and nature). The methods of the study were a field-based and direct inspection of the structures. Also the inspection of the decorations (Chinese Knotting) was done using library research methods.

Due to avoiding utilization of human figures and abstaining from idolatry، decorations have specific geometry in Islamic art and architecture. One of the striking characteristics of the knots (girih) that has caused to dynamicity throughout its thousand-year history is its regeneration and diversification of the diverse geometric properties. Girih tiling decoration is part of geometric arts in the traditional buildings of the historic town of Masouleh dates back to eight hundred years. Traditional and local architects of this historical town have adopted special and intellectual plans for creating visual attractions in expression and creation of girih tiling in the walls of the monuments. One of these valuable solutions is diverse geometric decorations patterns. Since the main facades of the houses in this town are directly located in the sunrise direction and it is accepted landscape for the citizens of this historical town، so the artists have shown their art and style in this part of the monument and built beautiful and harmonic diverse wooden windows and variety of these patterns are seen in all five neighborhoods in this town. Girih tiling consists of straight and broken lines on a regular basis that could be reasonably expanded in the surface. In the present study، it has been tried to classify the decorations in girih tiling in the neighborhood of Masouleh and also investigate girih tiling including scrolls and edges، and also the role of decoration in this element. The methodology of the research is based on field study and direct observation of the monuments and decorations and taking image and converting into Auto CAD files with dimensional analysis. Also، for description of girih tiling، descriptive and library studies have been conducted. Questions that the research seeks to answer in this paper are: Can it be offered a defined pattern for opening girih tiling by analyzing of the decorations in neighborhood of Khanehbar in Masouleh? And also is the largest usage of the patterns seen in scrolls (middle or central plan)? Does scroll use most patterns in its margins? The girih tiling patterns of “gavarehbari” with “boteh jegeh” designs (paisley)، eight squares ornamental layout، rectangular، “hasht-chahr longeh tokhmedar”، and gavarehbari with the scales patterns are more common patterns. Fourteen patterns were seen in studying the girih tiling patterns employed in the combined windows that “alat jafari chokhati” and then rectangular tiling and seven and eight sides tiling patterns were common. The patterns used in the friezes are mostly eight squares layouts. The most common patterns in the margins are four- side tiling in all parts. Diverse patterns of girih tiling، besides with diverse combinations resulted from placing together and offering shapes in the friezes and marginal patterns have offered rich visual ornamentation in the historical city of Masouleh. Such studies aid reproduction of these patterns in the contemporary fine arts while preservation and documentation of the fine and visual patterns in the Iranian girih tiling.