Contemplating Islamic Geometrical Design

BEHIND THE AL-AZHAR Mosque in Cairo is a group of buildings built in the late 15th century by the famous Mamluk sultan (See image right), al-Asraf Qaytbay. It consists of a wikala (a medieval market or mall) and a sabil-kuttab. The latter building is a traditional Mamluk multi-purpose structure where, on the ground floor, behind a metal lattice screen is a drinking fountain (sabil). On the floor above, with double arches on both sides is a primary school (kuttab). The streetfacing walls of these buildings are richly decorated with geometrical designs. There are stone panels with designs framing doorways, the voussoirs above the windows and storefronts all have individual designs, and even the capstone in the star vault entrance to the mikala has a geometrical design. Between the sabil on the ground floor and the kuttab on the first floor is a geometrical panel that wraps around a corner, as can be seen in the photo. Some of the patterns are repeated but mostly the designs are all different from each other. What they have in common are two features that are characteristic of geometrical designs made during the reign of the Mamluk sultans (1250-1517 ad). First of all, the designs show only part of a larger composition; they invariably show only a half or a quarter of a traditional star design. Secondly, most of the designs have kite-shapes that serve as links in a chain, connecting the individual star designs.
The mikala and sabil-kuttab are from the very end of the reign of the Mamluks and built during a period that is commonly considered to be the apogée of Mamluk art and architecture: the reign of Sultan Qaytbay. This sultan com- missioned the construction of many beautiful buildings in Cairo and his patronage encouraged lesser sultans and emirs to do likewise, both during and after his reign. His mausoleum is one of the most refined buildings in Cairo; it is situated in the Northern Cemetery and is best known for its exquisitely decorated dome, which interweaves geometrical patterns with plant motifs.
On the exterior of the sabil-kuttab (See image left) is a number of stone panels that show details from larger geometrical star designs. The area directly around this relatively simple doorway has been elaborately decorated. All these have been further accentuated by the double interlacing stone banding. Above the stone banding and outside the frame of the picture is a huge floriated rosette of at least 150cm diameter. The stone ornamentation is there to draw attention to the doorway.

Above the doorway, on either side of the window, are two square panels: they are each other’s mirror image. These two panels are typical of Mamluk design because they show a detail of a larger composition. They do not show us traditional star designs: they only show us the areas between the star designs. This exact same panel also appears on the qibla wall in the mosque of Qiqmas al-Ishaq (built during the reign of Sultan Qaytbay), where it is painted in blue, gold and white. Similarly, the design on the lintel above the door appears on a much larger scale on the dome of the mausoleum of sultan Qansuh Abu Said in the northern cemetery of Cairo. Both these exam- ples indicate that certain designs were popular, or that the craftsman who was able to make these designs was popular. Per- haps the lesser emirs of sultans in Cairo wanted to bask in the reflected glory of Sultan Qaytbay by using the same designs that were on his buildings.
This is the panel (See image above) that appears to the right of the window in the previous image. The panel contains three design elements that have been assigned different colours for the purpose of this article. The blue lines belong to a star design-they show a quarter of a star on each corner of the panel. The red lines form independent “kite” shapes that act as links in a chain. They hold the elements in the composition together. The black lines reveal their shape and function less readily; this will become clear once the composition is reconstructed. In order to make a full blue star, the quarter sections have to be arranged in such a way that they all join. To do this, the panel has to be mirrored. In this closeup of the panel, the floral decorations become visible. Fivepetallcd flowers and traditional vine & leaf motifs fill up the spaces between the interlacing bands of the design. The use of floral and vegetal motifs is at the heart of traditional Islamic design. They provide a counterweight to the straight lines of a geometrical pattern.

There are many panels such as this one in Mamluk Cairo, although they vary in size, location and material. The main question that springs to mind is “why?” What was the reason that Mamluk craftsmen made panels that showed a detail of a larger design? It is a design style truly unique to the Mamluks. The panels demonstrate the skill and creativity of the craftsmen in Cairo at the time; they were truly masters of their trade. They were so well-versed in geometrical design that they were able to innovate the way it was presented and develop new ways of showing a traditional and familiar artistic expression.

The Mamluk craftsmen evidently wanted to create geometric designs that engaged the citizens of Cairo. By purposely showing a small part of a big composition, they challenge the passer-by in the streets of Cairo to complete the design in his mind. It is as if the craftsman is saying: “Here is a small detail. Let’s see if you can visualize what the complete picture looks like.” They challenged the citizens of Cairo to use their intellect, their memory and their creativity. They encouraged them to contemplate the geometric design and possibly, by doing so, allow them some time to reflect on something other than their daily, hectic environment. Medieval Cairo would have had the same bustle of activity as it has today. Walking through the city, you would pass dozens of buildings, some grand, some mundane. Many of these buildings are adorned with a great variety of geometrical designs. Medieval citydwellers would have been able to recognize the occurrence of the same designs on different buildings. The ubiquity of geometrical designs in the cities of the Islamic world shows that the people living in these cities had an affinity with geometrical design that is hard to appreciate for us living in the 2 ist century. The pervasiveness of geometrical design in medieval Islamic societies created in the mind of citydweller a profound familiarity with the wealth of different designs.

What, then, was the design that the craftsmen who made the twin stone panels wanted the citizens of Cairo to visualize? By mirroring one panel so that we get four quarters of the blue star design in the centre, the design reveals itself.

The blue lines (See image below) have created a ten-pointed star design in the centre. The red kite shapes occupy the space between the blue star designs; their task is to hold the composition together. The black lines are unusual because they themselves are not a recognizable element from traditional geometrical design. Their purpose is to create shapes that are recognizable, especially the so-called “bow-tie” shapes that feature where the red, black and blue lines meet.

Now that the complete design is visible, we know what a Mamluk craftsman from late 15th-century Cairo wanted us to see with our mind’s eye. The design that has been created by mirroring one stone panel can itself again be mirrored, and that new design can then be mirrored again. This process can be repeated infinitely, and it is the essential attribute of Islamic geometric design.
Fortunately, not all geometrical designs are as complex as those of the Mamluks. In most cases, craftsmen used geometrical designs for the ornamentation of a surface. Such designs commonly consist of one, two or three design elements that are combined and repeated many times. Usually these elements can be contained in shapes that can be repeated infinitely by being placed next to each other. Usually these elements are a square, a triangle or a hexagon. In the case of the Mamluk panel, the square was the element that allowed infinite repetition.

This design from the Alhambra in Spain (See image above) is made in incised plaster and covers an interior surface. It is constructed by the repetition of star designs to cover a large surface area. Here there are no kite-shaped links holding everything together-the design consists of uninterrupted bands that travel from the top to the bottom and from the left to the right of the wall.

When confronted with such an elaborate composition, one of the first questions that spring to mind is, “how did they do that?” “How did they achieve such perfection and regularity?” It is tempting for us in the 21st century to see Islamic geometrical designs and use our own tools of analysis to better understand these designs. But it is important to realize that traditional craftsmen were usually not numerate. They would not calculate angles in order to make their compositions: their knowledge of geometry was practical, not theoretical. Their tools of the trade were a compass and a ruler. With these tools they drew circles and lines and, by connecting intersections of these circles and lines, they created patterns. When we look at Islamic designs, beauty and complexity seem to go hand in hand. But are these designs complex because we do not have the same affinity with geometry as people in traditional Islamic societies used to have? Would what we consider to be complex also have been considered complex by medieval citizens of Cairo or Konya or Granada? Complexity, like beauty, is in the eye of the beholder. It is possible that they were able to see and distinguish aspects of geometrical patterns that we are no longer able to. This is certainly true of the geometrical panel from Cairo that we have looked at; it does not reveal its secrets readily. This is compounded by the fact that we are not accustomed to seeing geometrical designs on a daily basis, and do not have that familiarity that people would have had in traditional Islamic societies.

The perfection, regularity and harmonious proportion that is evident in the Alhambra composition was achieved by first constructing a simple foundation composition out of hexagons. This composition would not remain visible once the geometrical design was finished. The foundation composition or “grid” allows the craftsmen to place the composition on a surface and ensures that the size of the individual components is in an appealing proportion to the overall surface area. Just as medieval Islamic craftsmen used the grid system to construct a composition, this same design technique can be used to deconstruct a composition.

By looking at the design (See image below) and discovering where the design elements repeat, it becomes possible to see the hexagonal grid that was used-the red lines show its location. The craftsman would have used this grid before making the final design. It shows thai each hexagon contains the same design. The design that is used for this composition is a twelve-pointed star. The overall composition can be further deconstructed by looking at how the twelve-pointed star design in the hexagon is made.
Like all Islamic craftsmen, those in the Alhambra would have used a compass and a ruler to construct the grid and the design. All geometrical designs begin with a horizontal line on which a circle is placed. The craftsman will then decide whether to divide the circle into, for example 5, 6 or 8 equal parts. This decision will determine how the design will develop and whether the design will fit into a pentagon, a hexagon or a square. The composition from the Alhambra can be reconstructed by taking the same design steps that the craftsman would have taken. Follow the steps as the illustrations below, from left to right) indicate and you will have created the design.

* Draw a circle and divide it into 12 equal sections.

* Draw a hexagon that fits into the circle.

* Draw another hexagon in the circle as indicated.

* Draw two triangles that fit into the hexagon from image 1. Make sure that the triangles do not touch the circle.

* Draw two more triangles that fit into the hexagon from image 1. The lines that form the triangles extend to the edge of the hexagon.

All the necessary construction lines have been drawn.

* Now take a different pen or pencil

* Draw the star shape as indicated.

* Draw the second star shape as indicated.

* The complete design with construction lines

* The final design as it appears in the Alhambra.
This design sequence demonstrates that it is perfectly possible, and even easier to draw traditional designs in the same way that Islamic craftsmen have been doing for centuries. Mathematical calculations only help when we want to understand geometrical design in a way that appeals to our modern approach to geometry and mathematics. If we want to understand Islamic geometrical design as a traditional skill, it is necessary to be practical, not theoretical: we have to learn by doing.

In all geometrical compositions there are different layers on which the viewer is invited to focus. Some are immediately visible; others reveal themselves after closer observation. They all share their invitation to contemplate the design and what it represents and symbolises to each individual. They invite the viewer to contemplate issues such as the seen and the unseen, beauty and order, the infinitely small and the infinitely big, foundation and structure, and of course, the notion of creation itself. Different eras and regions in the history of the Islamic world have used geometry in their own specific ways to express these concepts and issues.

The small panel from Cairo and the composition from the Alhambra both invite us to contemplate the large and the small, the part and the whole. The panel from Cairo might be understood to convey this notion: “you will understand the complete design through understanding the significance of the small part and its role in the complete design.” The Alhambra composition might be understood to convey, “Do not stand too far back lest you only see the complete design. Do not stand too close lest you only see the detail.”

There is more that we don’t know about Islamic geometrical design than what we do know. Hardly any historical documentation exists of how craftsmen worked or how they interacted with their patrons. We don’t know what their status was in society or how knowledge was transferred among craftsmen and from generation to generation. Nor do we know whether the craftsmen who made geometrical designs on walls were also able of making designs for a curved surface, like a dome. The challenge that the lack of historical written information poses to Islamic art and architecture in general is the need to learn by looking at the buildings and objects themselves. They have a great deal of information to give us if we look closely and look with an open mind.

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    A piece previously published in the print issue of Islamica Magazine between 2003-2009. The following has been an effort to digitize and archive as a free service. Author citations can be found at as we continue to work on improving the digital archives here.

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