THE SYSTEMS OF PROPORTIONING IN MEDIEVAL MUSLIM ARCHITECTURE

AbstractIn the pre-modern Muslim world important developments in the field of geometry occurred and a continuation of the classical traditions of proportioning prevailed in architecture. However, our knowledge of Islamic geometry as an independent discipline is more substantial than in the application of this knowledge in architecture. There is no medieval text that discusses the process through which geometric knowledge were transferred to architecture design, and contemporary sources are rather silent regarding the role assigned to geometry in the evolution of the design traditions of Muslim architecture. This situation has led to recent studies trying to make analysis of the geometrical principles encountered in the surviving drawings and the original work of architecture. This paper presents a fresh interpretation of such analysis and tries to identify two of the methods used in proportioning. The first method demonstrates the application of mathematical relationships to relate the parts of the design to the whole, while the second is the use of primary grids as a tool for measurements and proportion. In this method the setting-up of gridline network derives from geometric patterns serving as basic modular units.

1. IntroductionIn the pre-modern Muslim world important developments in the field of geometry occurred and a continuation of the classical traditions of mathematical proportions prevailed in architecture.

The development of geometry and other scientific fields of inquiry in the Islamic world were initiated during the eights and ninth centuries by translations from ancient texts such as Greek and Sanskrit. By the tenth century, original Muslim contributions to the sciences became significant; in this context important development in the field of geometry and mathematics resulted from the work of, Umar al-Khayyam, Abu’l Wafa al-Buzjani, Abu Mansur al-Khwarazmi, ibn al-Haytham and others. However, our knowledge of geometry as an independent discipline is more substantial than its application in architecture.

Although the available knowledge of the developments in the field of geometry in the pre-modern Islamic world is considerable, we don’t know enough about the process through which theoretical knowledge of geometry was transformed to architecture. The use of geometrical knowledge in practical sense had been confined to the medieval working methods of apprenticeship as found in the original documents including technical workshop literature, manuals of applied geometry and workshop drawings.

The available original documents include either written or drawn material. The written material is mainly the work of mathematicians who focused on the direct application of geometric shapes in decorative patterns. Muslim mathematicians such as al-Buzjani (d.998) wrote manuals explaining basic principles of geometric patterns and their applications in architecture. These manuals, which were intended for architects, craftsmen and building supervisors, discussed issues including the composition of two-dimensional decorative pattern. The drawn material consists of the surviving original drawings on scrolls, which illustrate plan drawings and decorative designs unaccompanied by any explanatory text (Fig: 4).

It is noted that the medieval Muslim master builder who was skilled in engineering/geometry (muhandasi), building (mi’mari) and also in drawing (tarahi),

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did not write as Vitruvius in the antiquity or Alberti and Palladio in the Renaissance did. As a result there is no available text that discusses the process through which geometric knowledge were transferred to architecture design, and little is known regarding the role assigned to geometry in the evolution of Muslim architecture.

As a result contemporary sources too are relatively silent about the use of geometric pattern as a governing tool of proportion in architectural design, and our knowledge about the degree as to which Muslim architects were informed of the theoretical developments in mathematics and geometry remain incomplete. This situation has recently encouraged analysis of the geometrical principles used in the surviving Muslim drawings and the original work of architecture. This paper presents a fresh interpretation of such analysis and tries to identify the principles of proportioning used in Muslim architecture.

2. Methods of proportioning in pre-modern Muslim architectureAnalysis of surviving pre-modern Muslim drawings and original work of architecture indicated that proportioning was used since the 9th century to relate all the different parts in buildings and to integrate the parts into the whole. Several methods of proportioning were based on mathematical relationship such as the golden ratio in the Great Mosque of Kairouan (Boussora and Mazouz: 2006); the relationship between the side of a square and its diagonal as in the case of the Great Mosque at Cordoba (Fernandez- Puertas: 1994); and the use of modular grid system in 15th century Timurid drafting as in Tashkent scrolls (Necipoglu: 1992). With view of their significance in identifying the systems of proportion in medieval Muslim architecture, this paper considers the last two of these examples.

2.1. Method I: The mathematical relationship of the square and its diagonal

The first method of proportion is based on the mathematical relationship between the side of a square and its diagonal. If the side of a square is given the conventional value = 1, its diagonal will have the value of √ 2. An arc is then drawn from the √ 2 diagonal of the square. From the point where the arc intersects the extension of one side of the square, a rectangle is then formed with sides in the proportion of 1: √ 2 and this rectangle will have a diagonal of √ 3. By repeating the same operation using the √ 3 diagonal a further rectangle is drawn with proportions of 1:√ 3 and so on.

This system was used as a governing method of proportions throughout mosque buildings since Umayyad architecture in the 8th century. One example of its application is found in the Great Mosque in Cordoba cited in Fernandez- Puertas (1994). Its traditional square plan was enlarged twice, in the 9th and the 10th centuries. Using the arc drawn from the diagonal of the square, the Great Mosque at Cordoba was enlarged from the square first to a 1: √ 2 rectangle and further a 1:√ 3 rectangle (Fig: 1, 2).

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Fig. (1) Plan of the Great Mosque, CordobaFernandez- Puertas (1994)

Fig. (2) Diagram of the original mosque extensionFernandez- Puertas (1994)

Another example of using the mathematical relationship of the diagonal of the square in setting proportions is found in the minaret of the Khanqa of Farag ibn Barquq in Cairo (Fig: 3).

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Fig. (3) The minaret of Farag ibn Barquq Khanqa, Cairo.

The empirical analysis by Ibrahim & Mostafa (1992) shows that the height of the minaret (H) equals 8 times the measurement of the side of its square base (F), thus H=8F. The illustration shows the minaret is divide into 8 equal square divisions each measures (F), and arcs drawn from the √2 and √ 3 diagonals.

The diagonal method was used in setting-up mathematical proportions in the design of the minaret. As the illustration in (Fig: 3) shows, the intersecting points of the arcs drawn from the square diagonals mark the positions of the various architectural elements of the minaret such as the base line and the top of shafts and locations of muqarnas and so on.

2.2 Method II: The modular geometric pattern and gridlines network The other method of proportion uses a primary grid system which is based on modular geometric units. It is recognized that the use of gridline system was found to be a common feature of architects' drawings in the 15th and16th century. All drawings are executed across a grid of squares (42- 62 mm), which represent the structural modules of the plan. Not only that but surviving buildings in Central Asia since the 9th century onwards were found to conform to such system that there seems no doubt that this was the method by which buildings were designed, drawn and set out (Rai: 1993; Tabaa: 1987).

The use of gridlines as a basic design tool in Muslim architecture is found in a group of 16th century architectural drawings from Bukhara. The drawings include plans drafted on square grid formulating modular units, which seem to be based on smaller basic units of geometric patterns. Islamic geometric pattern was broadly used since the 14th century in the planning, construction and decoration of Timurid/Turkmen architecture, not for decorative purpose alone as contemporary sources assume. In her discussion of the functions of decoration in Muslim architecture, Golombek (1988) refers to the existence of a primary grid that underlies all decoration and remains almost visible in the final product. This grid is related to the orthogonal grids used by Muslim architects to design plans and elevations of buildings. She deducted from these observations that primary grids which assisted in the design and construction of the building became the starting point of all decorations.

The thesis of this study suggests, by contrast with Golombeck’s interpretation, that the setting out of primary grids which assisted in the design and construction of buildings was based on modular units derived from geometric patterns rather than the other way round as Golombeck suggested. In other words geometric pattern was used as modular units for setting out the regulating gridlines.

This assumption is supported by the example from the 15th century Timurid/Turkmen scroll (Victoria and Albert museum no. 24, London- Photo: Hugh Sainsbury) presented by Necipoglu (1992) (Fig: 4). The Timurid/Turkmen scroll shows ground plans, inscriptions and decorative brick patterns on squared paper. The three illustrations are drawn on one grid system following a simple ratio of 2:1:2:1:2:1. The fact that the hidden vertical grid system is shared by the ground plans, as well as the inscriptions and decorative brickwork, indicates the dependence of such system on the geometric pattern acting as basic modular units. The grid system functioned as a drawing tool for setting measurements, and providing integrated proportions and unity of design.

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3. ConclusionsThe development of geometry, and other scientific fields of inquiry, in the Islamic world was initiated during the eights and ninth centuries by translations from ancient texts especially Greek. By the tenth century original Muslim contribution became significant. Hellenic and Muslim scientific discoveries were transmitted into the West in the twelfth and thirteenth centuries when Europe came into full contact with the Islamic centers of learning in Spain.

We know that the writings of Vitruvius in the first century AD were rediscovered in the renaissance. His well known treatise De architectura constituted the basic design principles up to present time. This paper helped demonstrating that Muslim architects had known the classical basic design principles centuries before the

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Fig. (4) Ground plans, inscriptions and decorative brick patterns on squared paper.Victoria and Albert museum, no. 24, London ( Photo : Hugh Sainsbury )

renaissance and used them in advancing their own methods of proportion in architectural design. However, we do not know of any Muslim text that makes reference to Vitruvius theories and we are not certain whether his treatises were translated into Arabic.

Significant influence of Muslim architecture on Europe is found in Gothic architecture. In Gothic architecture as well as in Muslim architecture, obvious unity and regularity were achieved by a due observance of the Classical principles of proportions, regulating grid lines were used as a modular tool. This similarity suggests that the classical design principles and Muslim contributions were transformed into Europe at least three centuries before they were discovered in the renaissance. It also support the assumption that Vitruvius treatises were translated into Arabic and then into Latin before they were finally transmitted to Europe. This important part of Muslim history, which is crucial for understanding the development not only of Muslim architecture but the architecture of the world remains to be verified by future research.

ReferencesFernandez- Puertas, Antonio (2002). Spain and North Africa. In The Mosque,

History, Architectural Development & Regional Diversity (ed.), Thames & Hudson Ltd and the American University in Cairo Press, Cairo, Egypt.

Golombek, L. (1988). The Function of Decoration in Islamic Architecture. In Theories and Principles of Design in the Architecture of Islamic Societies (ed.), a Symposium held by the Aga Khan Program for Islamic Architecture at Harvard University and the MIT, Cambridge, Massachusetts, USA.

Ibrahim, Abdelbaki M. & Mostafa, Saleh L. (1992). Principles of Architectural Design and Urban Planning During Different Islamic Eras. Organization of Islamic Capitals and Cities, Jeddah, Saudi Arabia.

Necipoglu, G. (1992). Timurid Art and Culture: Iran and central Asia in the fifteenth century. E.J.Brill.

Rai, J. (1993). Mathematics and aesthetics in Islamic architecture: Reference to Fatehpur Sikri.King Saud Univ. Vol. 5, Architecture and Planning, pp 19- 48, Riyadah.

Tabbaa, Y. (1987). Geometry and Memory in the Design of the Madrasat al-Firdows in Aleppo. In Theories and Principles of Design in the Architecture of Islamic Societies (ed.), a Symposium held by the Aga Khan Program for Islamic Architecture at Harvard University and the MIT, Cambridge, Massachusetts, USA.

Dr. Fathi BashierAssoc. Professor of ArchitectureSchool of Architecture and Environmental PlanningSharq Al-Neel CollegeKhartoum North.e-mail: <bashierfathi@hotmail.co.uk>

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