"Hasba" The Method of Drawing Islamic Geometric Patterns in Morocco in Comparison with the Traditional Iranian Radial Method

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.