Designing geometric designs

Niki Gamm

CNN International had an item this week on the use of Arabic geometric design incorporated into architectural designs in order to fancy up buildings in the United Arab Emirates. The designs were taken from traditional lattice work windows that allowed defuse light inside and kept windows cool without having to resort to air conditioning. Geometric design has been a part of Arabic art as far back as anyone can trace it and certainly its use proliferated in the century following the proclamation of Islam. Although few artifacts remain in the Arabian Peninsula prior to Islam, there is no reason to think that geometric design immediately appeared there after 622 AD.

Once the Arab tribes left the peninsula in search of conquest and to spread their new religion they would have encountered the use of geometric designs in the various structures built by the Romans and the Byzantines. For example, the Romans enjoyed mosaic floors, many of which were framed by geometric designs. The Arabs also inherited many of the works of ancient Greek mathematicians such as Apollonius, Pythagoras and Euclid in the field of geometry. In fact they solved a number of the problems which the Greeks had been unable to do. Seyyed Hossein Nasr has pointed out that “they devoted special attention to the symbolic aspects of geometry and its role in art and architecture, keeping always in view the qualitative geometry which reflects the wisdom of the ‘Grand Architect of the Universe.’”

The high regard in which geometric design was held has often been attributed to the supposed prohibition of depictions of the human figure. This is not exactly true. Figures of humans have been found in the palaces of the Umayyid caliphs. However, religious scholars finally agree that human figures could be shown as two-dimensional forms and hence would not usurp the place of God who alone could create man. But this decision was made long after geometric design began to be adopted primarily for the exteriors of buildings.

Ornament in very precise way

This prohibition against the human form had the effect of creating a type of art that could be understood and accepted wherever Muslims were located whether it be in Central Asia or Malaysia. The abstract patterns were seen as preventing the believer from entering some imaginary world by organizing architecture and ornament in very precise ways.

The circle serves as the basis for the patterns that adorn mosques, medreses (schools) and tombs as well as smaller works of art such as wooden boxes, carpets and doors. Repetition, symmetry and change of scale work together in creating varying effects that depended on the ability and creativity of the artist whose name is almost never known. Moreover the patterns could be expanded or contracted depending on the space to be filled. Using different shades of dark and light colored materials was used to achieve different effects.

According to J. Bourgoin, the geometric patterns can be divided into eight main categories: hexagons; octagons; dodecagons; combinations of stars or rosettes with two different numbers of points; combinations of squares and octagons; combinations of stars or rosettes; heptagons and pentagons. Geometric shapes are not just what they appear to be but they had and still have in Islam symbolic meanings. They are symbols that echo an overall, transcending unity. The Kaaba is a square that is repeated in courtyards and buildings and it is the earthly image of the quadrangular temple of paradise. Mosques are built as octagons not just so that the dome can rest securely upon them but they also reflect the Divine Throne which is supposed to be supported by eight angels. As Nasr writes, “The dome is not just a way to cover the walls. It is the image of the vault of heaven and beyond it of the infinite and illimitable world of the Spirit of which the sphere or circle is the most direct geometric symbol.”

Nasr continues to explain that geometric shapes fulfill an architectural function and going further, they reminded “man through their symbolic aspect of the spiritual principles which the traditional building or garden or landscape reflects on its own level of reality and which also corresponds to an inner state of man himself… In short, nothing is ever divorced from meaning.” His words are similar to those found in the 10th century Rasa’il Ikhwan aş-Şaf or Epistles of the Brothers of Purity which he also translated. “Know, oh brother… that the study of sensible geometry leads to skill in all the practical arts, while the study of intelligible geometry leads to skill in the intellectual arts because this science is one of the gates through which we move to the knowledge of the essence of the soul, and that is the root of all knowledge.”

Islamic designs are mathematically sophisticated patterns when we observe the ways in which they are interlaced. They are seen as the most direct expression of the idea of Divine Unity. This is another of Islam’s ideals – al-tawhid, the doctrine of unity or multiplicity in unity. The symmetry which the geometric patterns offer can go on to infinity, and complex, regular polygons such as a five-pointed star in a circle are the largest class of patterns that are found in interlacement. Nasr has been openly critical of western scholars who have taken the geometric patterns as decorations rather than as sacred art. “Islamic art is beginning to be understood for what it is, namely a means of relating multiplicity to Unity by means of mathematical forms which are seen, not as mental abstractions, but as reflections of the celestial archetypes within both the cosmos and the minds and souls of men.”

Peter J. Lu has been able to prove that medieval Islamic geometric designs were basically patterns that modern mathematicians were only able to describe in the second half of the 20th century. What he found was geometric design elements for elaborate, non-repeating patterns. It is easy to repeat patterns – one has only to look at wall paper for example. But it is much more difficult to provide a pattern that doesn’t repeat itself no matter how far it extends. In one instance that Lu cites, more than 20,000 templates were identified in a design.

No one would expect a craftsman 500 years ago to be able to determine the theoretical mathematics needed to make such non-repeating designs. But at least one design book has been found at Topkapı Palace that lays out design principles from the Timurid period (ca. 1370–1507). Presumably there are more to be found.

Source: Hurriyet Daily News, Nov. 24, 2012

Posted in: Architecture, Geometry, History, Islam