Advanced maths in medieval architecture

In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings

In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognised patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century.

A new study shows that the Islamic pattern-making process appears to have involved an advanced math of quasi crystals, which was not understood by modern scientists until three decades ago. The findings have been reported in the current issue of Science.

Two years ago, Peter J. Lu, a doctoral student in physics at Harvard University, was transfixed by the geometric pattern on a wall in Uzbekistan. It reminded him of what mathematicians call quasi-crystalline designs. Lu set about examining pictures of other tile mosaics from Afghanistan, Iran, Iraq and Turkey, working with Paul J. Steinhardt, a Princeton cosmologist who is an authority on quasi crystals.

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In their report, Lu and Dr. Steinhardt concluded that by the 15th century, Islamic designers and artisans had developed techniques “to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before discovery in the West.”

Some of the most complex patterns, called “girih” in Persian, consist of sets of contiguous polygons fitted together with little distortion and no gaps.Lu found the interlocking tiles were arranged in predictable ways to create a pattern.

The geometric star-and-polygon girihs, as quasi crystals, can be rotated a certain number of degrees to positions from which other tiles are fitted. This makes possible a pattern that is infinitely big and yet the pattern never repeats itself. This was, the scientists wrote, “an important breakthrough in Islamic mathematics”.

Lu and Steinhardt determined that the technique was fully developed two centuries later in mosques, palaces, shrines and other buildings.