Medieval math feat

New Delhi, Feb. 23: Intricate tile patterns that adorn a Mughal-era mausoleum in Agra and other medieval Islamic architecture scattered across Asia show that their designers had applied an advanced geometry 500 years before modern mathematicians discovered it, two US physicists said today.

The decorative patterns on the walls of medieval structures in Turkey, Iran, India and elsewhere in West and Central Asia exhibit what scientists call decagonal quasicrystalline geometry — a concept demonstrated by Western scientists only after the 1970s.

Physicists Peter Lu from Harvard University and Paul Steinhardt from Princeton University analysed hundreds of photographs of tilework on the walls or ceilings of mosques, madarsas, and shrines in the region.

Their findings, which appear today in the US journal Science, suggest artisans may have created the elaborate decagonal patterns using a special set of polygonal tiles.

“This is concrete evidence for a high level of geometric sophistication,” Lu told The Telegraph. “Decagonal geometry is an idea in the history of thought and it was being used five centuries before modern science discovered it.”

Researchers have until now believed that medieval artisans had created the geometric patterns using a straight edge and compass. But Lu and Steinhardt have said that by the 13th century, there was “an important breakthrough” in Islamic mathematics and design — the discovery of an entirely new way to construct patterns using a set of special tiles called “girih” tiles.

“We’ve found widespread evidence for the same approach being used across the Islamic world,” Lu said. “Again and again, girih tiles provide a logical explanation for complicated patterns.”

The 1405 AD Timurid Tuman Aga mausoleum in Samarkand, Uzbekistan, the 1496 AD Darb-i-Kushk shrine in Isfahan, Iran, and the 1622 AD I’timad-al-Daula mausoleum in Agra, India, are among the structures displaying decagonal geometry.

The girih tiles would have allowed the artisans to create the complex geometry including a nearly-perfect quasi-crystalline pattern on the 1453 AD-Darb-i-Imam shrine in Isfahan, Iran, the researchers said.

Quasicrystalline tiling was first described in the West only in the 1970s by British mathematician Roger Penrose and later by others over the past three decades.

The physicists speculate medieval architects and mathematicians may have been engaged in dialogue. “It wouldn’t surprise me if the concept of girih tiles emerged out of such a dialogue,” Lu said.

Lu, a graduate student in physics, says the project to analyse tile patterns in the medieval Islamic architecture emerged from a trip to Uzbekistan where he spotted the decagonal patterns.

For his physics research, Lu designs experiments to be conducted on the International Space Station. He’s hoping his research may contribute to changing perceptions about the Islamic world.

“Five hundred years ago, they appear to have been way ahead,” Lu said.