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December 2007
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Islamic Architecture

Penrose Geometry Evokes New Interest
By Sameen Ahmed Khan

Islamic art traditionally uses a mixture of calligraphy, geometric and floral designs because of a prohibition on the portrayal of the human and animal forms. The medieval Islamic artists produced intricate decorative patterns using very sophisticated geometrical techniques. In keeping with the Islamic tradition of not depicting images of people or animals, many religious buildings were decorated with geometric star and polygonal patterns, often overlaid with a zigzag network of lines. All historians have until now assumed that the intricate tile work was produced using straight edges (rulers) and compasses. Recent studies have altered this long held view bringing recognition to the mathematical intuition of the artists and possible collaborations with the mathematicians of the time. The new finds reveal that these patterns were created using a set of just five special template tiles (different shapes including, the decagon, pentagon, diamond, hexagon and the rhombus) developed around the 13th century. These elaborate patterns are known as girih. The girih designs have the quasi-crystalline symmetry. The principles behind quasi-crystalline symmetry were calculated by the Oxford mathematician Roger Penrose in the 1970s and were first described by Penrose in the guise of the famous Penrose tiles.

The patterns observed in the medieval Islamic architecture could not have been produced by the artists without a deeper knowledge of geometry. This indicates intuitive understanding of complex mathematical formulae, even if the artisans had not worked out the underlying theory, the study says. The research shows an important breakthrough had occurred in Islamic mathematics and design by the 13th century. Peter J. Lu of Harvard University and Paul J. Steinhardt of Princeton University recently published several articles describing their discoveries of the sophisticated geometry used in the Islamic architecture. Peter Lu who designs physics experiments for the International Space Station became interested in the subject while traveling in Uzbekistan as a tourist, after a trip to a space facility in Turkmenistan. In Uzbekistan, he noticed a 16th century Islamic building with decagonal (ten-sided polygon) motif tiling. He immediately recognized the designs as the Penrose tiling. This inspired him to search through thousands of photographs of Islamic patterns and led him to a wall of the Darb-i-Imam shrine in Iran, built in 1453. He also studied the 15th century Timurid-Turkmen scroll now held by the Topkapi Palace Museum in Istanbul, Turkey. His study reveals that the above patterns use the principles of quasi-crystalline symmetry, established centuries later by modern mathematicians. Now, it is very clear that the Islamic artists were creating patterns with quasi-crystalline symmetry more than 600 years earlier. In recent years it has been observed that the positions of atoms in a metallic alloy have a quasi-crystalline structure.

One may wonder as to how the very complex patterns could be produced by the workers? Creating a quasi-crystalline pattern would have been done using different combinations of the girih tiles. Each tile is decorated with several lines, and when the tiles are laid edge-to-edge the lines connect to form a continuous pattern; something that researchers believe could be done by a worker with little mathematical training. Artists could have used holes in the template tiles to trace a design on to a surface, which would be made into a mosaic. The researchers have demonstrated how the different combinations of the girih tiles can be used to create the very wide range of complex patterns found in the Islamic architecture.

(The author teaches at Salalah College of Technology, at Salalah, Oman)


On the authority of Abu Hurayra, the Prophet (Pbuh) is reported to have said, “The poor will enter Paradise five hundred years before the rich. In the reckoning of Paradise this equals one half of a day.” On the authority of ‘Abdallah, the Messenger of God (Pbuh) is said to have observed, “The indigent one is not he who wanders about hoping to be thrown a mouthful or two, or a date or two.” Someone asked, “Who then is the indigent one?” He replied, “He is one who cannot meet his essential needs and who is ashamed to beg from men, nor are they aware of him so that he might be given charity.” This saying, “He is ashamed to beg from men,” means that he is ashamed before God to beg from men, not that he is ashamed before men.