Intricate decorative tilework found in medieval architecture across the Islamic world appears to exhibit advanced decagonal quasicrystal geometry - a concept discovered by Western mathematicians and physicists only in the 1970s and 1980s. If so, medieval Islamic application of this geometry would predate Western mastery by at least half a millennium.
The finding, by Peter J. Lu at Harvard University and Paul J. Steinhardt at Princeton University, will be published this week in the journal Science.
"We can't say for sure what it means," says Lu, a graduate student in physics at Harvard's Graduate School of Arts and Sciences. "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. It would be incredible if it were all coincidence, though. 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."
"We're finding widespread evidence for the same approach being used for 500 years across the Islamic world," says Peter J. Lu, a graduate student in physics. "Again and again, girih tiles provide logical explanations for complicated designs." 
