Tile surface designs show Islamic mathematical might

[Al-khiyal]

Washington • Designs on surface tiles in the Islamic world during the Middle Ages reveal their makers’ understanding of mathematical concepts not grasped in the West until 500 years later, according to a U.S. study published yesterday. Many medieval Islamic buildings’ walls have ornate geometric star-and-polygon, or “girih,” patterns, which are often overlaid with a swirling network of lines. Researchers widely believed medieval artisans made the patterns with a straightedge and compass.

But Peter Lu of Harvard University and Paul Steinhardt of Princeton University, writing in the journal Science, found that “by the 13th century artisans had begun producing the patterns using a small set of decorated polygonal tiles, which the authors term ‘girih tiles,’” according to a statement by journal’s publisher, the American Association for the Advancement of Science.

“This girih tile method was more efficient and precise than the previous approach, allowing for an important breakthrough in Islamic mathematics and design,” the statement said. “By the 15th century the tiled patterns had become extraordinarily complex and a handful of them were what mathematicians today call ‘quasicrystalline’ designs.”

These mosaics are formed from five polygons — a decagon, a pentagon, a lozenge, a hexagon and a triangle — each representing a unique decorative motif. The technique, which shows an important mathematical and design advance in the medieval Islamic world, allows for the creation of designs to infinity which do not repeat and which have a perfect 10-sided symmetry. The concept was first demonstrated in the West in the 1970s by British mathematician Roger Penrose.

Tile surface designs show Islamic mathematical might

[Al-khiyal]

Harvard University's Peter Lu and his cousin, Christina Tam, visit a tile-covered shrine in Bukhara, Uzbekistan. The wondrously intricate tile mosaics that adorn medieval Islamic architecture may cloak a mastery of geometry not matched in the West for hundreds of years

WASHINGTON - Those wondrously intricate tile mosaics that adorn medieval Islamic architecture may contain a mastery of geometry not matched in the West for hundreds of years.

Historians have long assumed that sheer hard work with the equivalent of a ruler and compass allowed medieval craftsmen to create the ornate star-and-polygon tile patterns that cover mosques, shrines and other buildings that stretch from Turkey through Iran and on to India.

Now a Harvard University researcher argues that more than 500 years ago, math whizzes met up with the artists and began creating far more complex tile patterns that culminated in what mathematicians today call “quasicrystalline designs.”

An intricate strapwork pattern covers an interior archway in the Sultan's Lodge in the Green Mosque in Bursa, Turkey, dating to the year 1424

Quasicrystal patterns weren’t demonstrated in the West until the 1970s.

“It shows us a culture that we often don’t credit enough was far more advanced than we ever thought,” contends Harvard graduate student Peter J. Lu, who studied the question after a vacation in Uzbekistan left him marveling at the tilework.

This isn’t run-of-the-mill geometry. Quasicrystals are made by fitting together a set of shapes, including five- and 10-sided shapes, into patterns that, unlike typical tile floors, don’t repeat.

In Friday's edition of the journal Science, Lu and Princeton physicist Paul Steinhardt report finding a set of polygon-shaped tiles — a decagon, pentagon, diamond, bow tie and hexagon — that were arranged into distinctive patterns found on major Islamic buildings from the 12th through 15th centuries.

Examining architectural scrolls that were essentially training manuals for the time period, he found hand-drawn outlines of the five shapes. And when he combed through thousands of photos of medieval Islamic buildings, he found that same set of shapes increasingly used over the years to make ever-more complex patterns, including a seemingly true quasicrystal by 1453.

It’s not the first time such a link has been suggested.

But if it’s right, “this would be a hitherto undiscovered episode in the spectacular developments of geometry in central Islamic lands ... achieved by artisans probably inspired by theoretical mathematicians,” said Islamic art specialist Oleg Grabar.

Geometry feat cloaked in medieval Islamic tile

[Al-khiyal]

Science Magazine