CC BY
38УДК 72.012.6
Mustafoev Sh.Sh.
Graduate student (PhD) Tashkent Architecture and Construction Institute.
Department of History and Theory of Architecture (Tashkent, Uzbekistan)
CONSTRUCTION OF THE "GIRIH" - GEOMETRIC PATTERN.
BASED ON "BUKHARA SCROLLS"
Abstract: In this article, we discuss the principles of construction, compilation, and geometric analysis ofgirths, based on the manuscripts ("daftar - i girih") of architects of the 16th century. Objects of the research are based on the architectural scrolls, archival materials, knowledge base and unique skills of traditional artisan masters of Uzbekistan. Furthermore, in the article, we develop a hypothesis about the construction of girihs and bring several examples from the manuscripts of the ancient artisan masters of Central Asia.
Key words: daftar-i girih (Bukhara scroll - manuscript), architectural decoration, Girih (Aqd), arabesque, epigraphy, geometric analysis, rapport.
Introduction. If we investigate ornaments in our cultural heritage dividing them into three main groups (Islamic, geometric, epigraphic), we could discover that the geometric ornaments are an indispensable part of all of them.
Nowadays there are many types of errors and problems in the creation of geometric patterns, but also in the process of their restoration (Fig. 1). Based on our investigation, we could claim that one of the main reasons consist that our specialists cease to learn from the knowledge and skills of artisans who have worked in this field and made construction, restoration, architectural works based on geometric analysis.
Figure 1. Types of errors and problems in the creation of geometric patterns. Entrance
portal of the Guri Amir mausoleum in Samarkand. The geometrical analysis was made by Sh.Sh.
Mustafayev.
_
Fig. 2. Samarkand. The entrance portal of the Sherdor Madrasah on Registan Square. Photo by Sh.Sh. _Mustafayev.._
Body. Girih [15, p.579.] (Aqd [20, p.109.]) comes from the Persian word knot, which means tangled [7, p. 105.]. Different types of Handasa (Handasiy naqsh) [8, p.70.] have been widely used in architecture, arts and crafts, etc.
The creation of geometric surfaces and the construction of girihs have been known to humanity since the past, and the researches for the secrets of their creation intensified in the early XVDI century. A striking example, who studied the girikhs in his works, can be cited such scientists as: M.S. Andreev [1], N.B. Baklanov[2], G.I. Gaganov[6], L.I. Rempel[13], G.A. Pugachenkova[11], M.S. Bulatov[5], B.N. Zasypkin[27], Z. Bosithonov[3], Miroslaw Majewski[21], Gulru Necipoglu[18], Sarhangi, Reza[23], Hattstein Delius[19], Lu P. J. [22], Sebastian R. Prange[24], Koliji Hooman[20].
Based on our investigation creation of the girihs is based on the rapport [10] (triangles, rectangles, hexagons, and other types of polygons) which repeating in a certain rhythm (all of them have their mirroring part) (Fig. 3). If we look at the methods of geometric analysis of the rapport's fragment and solutions of "knots", we could see that scientists had developed their own hypothesis to solve the secret of the mirroring part. Such as analyses based on mathematical 5
calculations [5], analyses using circles (circles and rulers) [3], a modular system - dividing the rapport into polygonal surfaces [12], and studies girihs using computer technology [15].
a
b
_i_d_
Fig. 3.
a - Samples from Topkapi scroll and analysis of hidden polygons in them. b - An analogue to the Topkapi scroll. Manuscript from about 10-13 th centuries. The performance of the girikh is described in Persian. Fi tadahul al-ashkal al-mutashabiha av al-mutafik page. National Library of France. c - Samples from Topkapi scroll and analysis of hidden polygons in them. d - An analogue to the Topkapi scroll. Around the 11th-13th centuries, a sample from the appendix to the folios of Buzjani. National Library of France. _The geometrical analysis was made by Sh.Sh. Mustafayev._
According to our research, the results of this analysis have their advantages and disadvantages. We found it necessary to rely on the knowledge and skills of the artisan masters who worked in this area to create the concept of the girih analysis. The aim of our research is to find out what the girihsaze (creation of girikhs) school is based on.
The object of our study is based on manuscripts of the Bukhara scrolls (XV-XVI c.) [9], Topkapi scroll (XVc.) [17], The Mirza Akbar Architectural (Muhammad Jafar) scroll (1840-1870) [28]. Rely on research results there were developed concepts of analyzing and constructing girihs:
1. Recurring (mirroring) part of the girih - to find out the rapport. The basis of any rapport is rhythmically repeating surfaces (even asymmetrical ones).
2. Divide the Rapport into specific segments (polygons) or circles and divisions, using the traditional method, depending on compositional requirements. It should be noted that at the heart of any polygon in the girih are circles and lines.
3. If we divide the sides of the separated polygons into particular segments (two, etc.) again, we could form stars from polygons. (Note that multi-layered girihs are created based on the rhythmic division of these stars into polygons repeatedly.)
Based on these three principles, we can say that the evolutionary development of the girikhs took place gradually, and because of evolution, multi-layered girihs were formed. That is, at the heart of each complex girih are hidden simple geometric shapes or polygons.
Let us consider a few examples as an argument for our theory, such as drawing number 2/3 from the Bukhara scroll (inv. n. - 4429/16.). At the first and cursory glance, we can say that the girih is drawn with a random course of lines and it is composed chaotically, but if you observe it carefully, you can see that the rapport of the drawing consists of a dodecagon, an octagon and two trapeziums in the form of bow, which is drawn for a screen or lattice. Geometric analysis is based on the above principle, and as a confirmation of our opinion has shown in (Fig. 4.) In which the geometric analysis is presented in stages.
A rare drawing from the Bukhara scroll (inv. n. - 4429/16.), drawing number 2/10 can serve as a vivid example of our theory. At a quick glance, this geometric ornament is similar to (Fig. 2.), and it seems that it does not consist of polygons, but the girih is built based on polygons repeating in a certain rhythm. Moreover, the pattern is based on three
repeating polygons like a hexagon, a rectangle, and a triangle (Fig. 5.). It can be seen that the repetition of the polygons in this tectonic order gave the girih a dynamic tone. In turn, this girih can serve as proof of the above concept.
Fig. 4. Bukhara scroll (inv. n. - 4429/16.), drawing number 2/3. The geometrical _analysis is made by Mustafayev Sh. Sh._
Fig. 5. Bukhara scroll (inv. n. - 4429/16.), drawing number 2/10. The geometrical
_analysis is made by Mustafayev Sh. Sh._
These combinations of girihs are widespread in the school of architects of Central Asia in the field of creating geometric ornaments, based on these theories and knowledge, it was easy to create new patterns, replacing the rhythmic arrangement of polygons (Fig. 6). It can be noted that during the reign of the Taurid dynasty, such combinations of girihs were widely used to cover large surfaces of architectural monuments (Fig. 2).
To find out the correctness of the theory we have created for the construction of girihs, let us look at the geometric analysis of the drawing from the Topkapi scroll №. 38. Girih, in some cases, could be considered multi-layered, which is based on two repeating rapports (consisting of a rectangle and a triangle) (Fig. 8.4).
If we analyze a rectangular rapport, we can do it by dividing the rapport into four more parts (which is just mirroring) (Figure 8.5). These parts of rapport in common consist of
dodecagons, pentagons, trapezoids, and octagon. There are four dodecagons placed on the edges of the rapport, so in the middle part located regular octagon and we could see irregular pentagons around the octagon. The three sides of the pentagon (red sides) are not equal with opposite two sides (that means pentagon does not irregular and the red sides are not even with the blue ones). In the next step, the stars were formed by dividing the sides of the polygon into two parts (Fig. 8.5). The inner parts of the polygons (stars and corners) in red and blue are extremely different from each other.
Fig. 8. Topkapi scroll, girih № 38. The geometric analysis is made by Sh. Sh. _Mustafaev._
Based on the above method, we could see that the geometric basis of the rapport in the form of a triangle consists of decagons, hexagons, and trapezoids. No, wonder the old masters placed even polygons at the corners of the rapport. One of the main reasons for this was that if you did not put even polygons at the edges, then the sides of the rapport would not be connected correctly and there would be large intermediate gaps between them. As a result, we would get a girih similar to the pattern at the entrance to the mausoleum of Khoja Akhmad in the Shahi-Zinda complex in Samarkand [12, fig.78], and the master would have problems in the process of installing ceramic tiles (Fig. 7). Based on the conclusions, we can say that the scrolls of this type were made by experienced specialists in their field, in addition, without knowing arithmetic, the architects would not have been able to create such wonderful architectural drawings.
Fig. 7. The entrance portal of the tomb of Khoja Ahmad in the Shahi-Zinda
complex in Samarkand. The geometric analysis was made by Sh. Sh. Mustafoev.
Conclusion. Based on the researches conclusion we could be say that geometric patterns, along with architectural monuments, have undergone a process of gradual development. During the period of primitive society, geometric patterns were very simple
and were widely used in applied arts [12, p.28.]. However, in the early middle Ages, girikhs had evolutionary developing process and that time based on circles they made patterns. They drew geometric ornaments, with the help of compasses and a ruler (which improved periodically) [14, p.77-93.]. Finally, the evolution of sciences such as algebra and geometry [18, p.11-78.] has helped artisan create perfect polygons and place them in a specific module. The gradual development of rapports and the splitting of polygons into smaller segments led to the formation of complex and multi-layered girihs. Based on the results of the research, the principles and theories we have created could be used not only in the geometric analysis of girihs but also in the restoration and creation of new geometric patterns.
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