Islamic artists in the 15th century used complex mathematical techniques that were unknown to Western scholars until the 1970s, a new study co-authored by a Harvard graduate student revealed.

According to Harvard doctoral candidate Peter J. Lu and Princeton University Professor Paul J. Steinhardt, the authors of the study, the motifs that embellish mosques and palaces throughout the Middle East and Asia demonstrate symmetrical patterns which were not associated with recognized mathematical formulas.

Islamic art typically incorporates sets of five template tiles—a decagon, pentagon, diamond, bow tie, and hexagon. These tiles are used to draw shapes onto the edifices of Islamic buildings, which create infinite symmetrical patterns that never repeat—a process known as “quasicrystalline tiling.”

“We can’t say for sure what it means,” said Lu, who is expected to receive his PhD in physics in 2007. “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.”

British scholar Roger Penrose was the first person to mathematically describe this concept in the Western world in the 1970s. Since then, the mathematical theory has been further refined by Steinhardt and Dov Levine, a physicist at the University of Pennsylvania.

The new study—to be published in the upcoming issue of Science—links geometric concepts to Islamic art.

The “girih tiles,” Lu and Steinhardt write, describe the Islamic patterns that may have served as models for creating huge masterpieces without the extensive and often inconsistent practice of separately drawing each line segment. Historians had previously assumed that artisans used straightedges and compasses to produce the ornate patterns.

“It would be incredible if it were all coincidence. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we thought,” Lu said over the weekend. “Again and again, girih tiles provide logical explanations for complicated designs.”

Prominent buildings throughout the Islamic world feature such configurations, ranging from mosques in Isfahan, Iran, and Bursa, Turkey to shrines in Herat, Afghanistan and Agra, India.

Lu said he detected the decagonal ornamentation on a 16th century Islamic building in Uzbekistan while he was in the region surveying a space center in Turkmenistan.

Lu added that he confirmed his observations with the help of the Harvard’s collection of Islamic art.

“You can go through and see the evolution of increasing geometric sophistication,” Lu said. “So they start out with simple patterns, and they get more complex.”

—Staff writer Sonam S. Velani can be reached at svelani@fas.harvard.edu.