ISLAM - 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 tilework 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 principal of non-repeating patterns on a flat surface is known as quasicrystal geometry. 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.
But two American mathematicians believe that near-perfect quasicrystal geometry was practised by Islamic scholars earlier than the 15th century when it was used to decorate the walls of important buildings.
Peter Lu of Harvard University and Paul Steinhardt of Princeton University said that 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.
"We can't say for sure what it means. 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 Lu.
"At the very least it shows us a culture that we often don't credit enough was far more advanced than we ever thought before," he said.
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 Steindhardt 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 decorative tilework had been created using straight edges and compasses but the study suggests the artisans were using a basic toolkit of girih tiles made up of shapes such as the decagon, pentagon, diamond, bowtie and hexagon.
"Straightedges 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," Lu said.
"Individually placing and drafting hundreds of decagons with a straightedge would have been cumbersome. It's likely they used particular tiles we've found by decomposing the artwork," he said.
Lu started to think about the mathematics of Islamic tilework on a visit to Uzbekistan. He embarked on a study of photographs of tilework and architectural scrolls from Iran, Iraq, Turkey and Afghanistan, including a 15th-century Timurid-Turkmen scroll held in the Topkapi Palace Museum in Istanbul.
The scientists found that by 1453, Islamic architects had created overlapping patterns with girih tiles at two different sites to produce near-perfect non-repeating quasicrystalline patterns.
"The fact that we can explain so many sets of tiling, from such a range of architectural structures throughout the Islamic world with the same set of tiles makes this an incredibly interesting universal picture," Lu said.
The scientists were able to match the girih tiles used for creating complex tilework with drawings in 15th-century Persian scrolls drafted by master architects. "We're finding widespread evidence for the same approach being used for 500 years across the Islamic world.," Lu said.