Islamic artists were 500 years ahead of Western scientists
By Steve Connor, Science Editor
The Independent | 23 February 2007
Islamic artists were exploiting a mathematical principle to decorate buildings with complicated patterns of tiles more than 500 years before its discovery in the West.
The decorative tile work that adorns some medieval Islamic buildings has been found to use basic geometric shapes that form a complex and highly intricate tiling pattern which does not repeat itself.
In modern mathematics the principle of non-repeating patterns on a flat surface is known as quasicrystal geometry, and the most famous example is known as Penrose tiling, after the Oxford mathematician Roger Penrose, who was thought to have discovered it 30 years ago.
However, two American mathematicians believe that near-perfect quasicrystal geometry was used by Islamic scholars earlier than the 15th century to decorate the walls of important buildings.
Peter Lu, of Harvard University, and Paul Steinhardt, of Princeton University, said advanced quasicrystal geometry based on 10-sided shapes is seen in the tiling patterns of mosques and madrasas of the Middle East and central Asia, predating its discovery by Western mathematicians by 500 years.
"It could be proof of a major role of mathematics in medieval Islamic art, or it could have been just a way for artisans to construct their art more easily," said Mr Lu. "At the very least it shows us that a culture we often don't credit enough was far more advanced than we thought before."
In keeping with the Islamic tradition of not depicting images of people or animals, many religious buildings were decorated with geometric star-and-polygon patterns, often overlaid with a zigzag network of lines.
Lu and Steinhardt show in a study published in the journal Science that by the 13th century Islamic artisans had begun producing patterns using a small set of decorated, polygonal tiles which they call "girih" tiles.
Art historians have until now assumed that the intricate tilework had been created using straight edges and compasses, but the study in Science suggests the Islamic artisans were using a basic toolkit of girih tiles made up of shapes such as the decagon, pentagon, diamond and hexagon.
"Straight edges and compasses work fine for the recurring symmetries of the simplest patterns we see, but it probably required far more powerful tools to fully explain the elaborate tiling with decagonal [10-sided] symmetry," Mr Lu said.
"Individually placing and drafting hundreds of decagons with a straight edge would have been exceedingly cumbersome. It's more likely these artisans used particular tiles that we've found by decomposing the artwork," he said.
The scientists found that by 1453, Islamic architects had created overlapping patterns with girth tiles at two sites to produce near-perfect quasicrystalline patterns that did not repeat themselves. "The fact that we can explain so many sets of tiling, from such a wide range of architectural structures throughout the Islamic world with the same set of tiles, makes this an incredibly interesting universal picture," Mr Lu said.
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