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Medieval Islamic architects were math whizzes

The walls of many ancient buildings in the Islamic world are covered in designs that are mind-bogglingly complex. A new study now helps explain how the designers managed to make such intricate patterns.

The patterns, called "girih," are made up of different forms of polygons, somewhat like the tiles on a typical modern-day floor, but many times more complicated. In some cases, another pattern is in the background and the lines of the polygons cut across this other pattern.

Some of the most complex patterns, which first appeared in the 13th century, involve mathematics that weren't discovered until the 20th century in the West.

Until recently, researchers generally believed that medieval Islamic artisans produced these patterns using a compass and ruler. But, the polygons have to be virtually perfect in order to fit so many of them together into patterns, so it's hard to imagine how people could have managed that with those tools.

New research by Peter J. Lu of Harvard University and Paul J. Steinhardt of Princeton University now suggests that around the 13th century, designers figured out a new method for making girih patterns that allowed them to design even more complicated versions.

Instead of using a compass and ruler, the designers began using a set of polygon-shaped tiles to trace the basic units of the patterns. This allowed them to get the shapes right every time. It also made the work easier, allowing the designers to think up even more sophisticated patterns.

The research appears in the 23 February issue of the journal Science.