http://discovermagazine.com/2008/jan/math-breakthrough-spotted-on-mosques
01.09.2008
59. Medieval Mosque Shows Amazing Math Discovery
The never-repeating geometry of quasi crystals, revealed 500 years early
by John Bohannon
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 repeat when infinitely
extended, its pattern maps onto Penrose tiles—components for making
quasi crystals discovered by Oxford University mathematician Roger
Penrose in the 1970s—in a way that is consistent with the quasi crystal
pattern.
Among the 3,700 tiles Lu and Steinhardt mapped, there are only 11 tiny
flaws, tiles placed in the wrong orientation. Lu argues that these are
accidents possibly introduced during centuries of repair. “Art
historians always suspected there must be something more to these
patterns,” says Tom Lentz, director of Harvard University Art Museums,
but they were never examined with “this kind of scientific rigor.”
Above videos:
1. A spandrel in the Darb-i Imam shrine in Isfahan, Iran (ca. 1453) and
overlay of the large- and small-scale pattern reconstructed with the
same girih tiles in various sizes—the only example of a nearly perfect
quasi-crystalline Penrose pattern.
2. Girih-tile reconstruction of a panel from the Gunbad-i Kabud tomb
tower in Maragha, Iran built in 1197.
3. External panel from the Mughal I'timad al-Daula Mausoleum in Agra,
India (ca. 1622), and reconstruction of the pattern using the girih tiles.
4. A panel of the Topkapi scroll in Istanbul, Turkey. The large girih
tiles subdivide into smaller ones to create overlapping patterns at
different length scales. This scroll was a user manual for architects
and contains designs that were widely used.
All animations courtesy of Peter Lu.
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