The mosques of the medieval Islamic world are artistic wonders and perhaps mathematical wonders as well. A study of patterns in 12th- to 17th-century mosaics suggests that Muslim scholars made a geometric breakthrough 500 years before mathematicians in the West.
Peter J. Lu, a physics graduate student at Harvard University, noticed a striking similarity between certain medieval mosque mosaics and a geometric pattern known as a quasi crystal—an infinite tiling pattern that doesn’t regularly repeat itself and has symmetries not found in normal crystals (see video below). Lu teamed up with physicist Paul Steinhardt of Princeton University to test the similarity: If the patterns repeated when extended infinitely, they couldn’t be true quasi crystals.
Most of the patterns examined failed the test, but one passed: a pattern found in the Darb-i Imam shrine (seen in the first video above), built in 1453 in Isfahan, Iran. Not only does it never ...
