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Science imitates art?

Artisans decorated the octagonal Gunbad-i Kabud tower in Iran (c. 1197 AD) with incredibly complex geometric patterns. On other medieval Islamic buildings, the same tiles were used to create intricate patterns reflecting mathematics that had not been understood in the West until British physicist Roger Penrose studied them in the 1970s and 1980s. A paper published last week in Science was the first to make this connection.

The five essential polygons


The pentagon (1), rhombus (2), hexagon (3), bowtie (4), and decagon (5) make up the set of five basic shapes used to create mosiac patterns.

Unique characteristics of the polygons


Create your own Medieval Islamic
design templates

With scissors, cut the shapes from the .PDF documents below. Collect as many individual pieces of each shape as you would like. Then, arrange them in patterns to create your unique medieval Islamic design. As a challenge, try to create a design by arranging all five shapes.
Gunbad-i Kabud tomb tower in Maragha, Iran, taken circa 1870s, by A. Sevruguin.
Gunbad-i Kabud tomb tower in Maragha, Iran, taken circa 1870s, by A. Sevruguin. (Harvard College Library)

Eight centuries later

Today, scientists use the geometric lessons of Roger Penrose to make quasicrystals: patterns of shapes that do not occur naturally among crystals, such as polygons with five or 10 sides. Materials with atoms in these special arrangements can have unusual properties, like a commercially available frying pan whose quasicrystal coating is harder than steel and as slippery as Teflon.

Templates used as design guides


This template, from a scroll now housed in Istanbul's Topkapi Palace, shows the same type of intricate geometric pattern as on the tower, built several hundred years earlier. These scrolls were used to transmit and document information among master architects.

Marveled at tilework

Visiting his cousin in the Peace Corps in 2005, Peter Lu was struck by the beauty of the decorations on a building in Bukhara, Uzbekistan. Lu, a PhD candidate in Harvard's physics department, thought the geometric patterns might be related to ones he had written about in his undergraduate thesis at Princeton - that he thought hadn't been discovered until the 1970s. Since then, Lu has spent hundreds of hours in the basement of Harvard's art history library, poring through pictures of Islamic art and architecture. His conclusion: The art, in countries from Iran to Turkey to Uzbekistan, ''reveals a much greater degree of mathematical sophistication than we had thought.''
SOURCE: Peter J. Lu and Paul J. Steinhardt; Decagonal and Quasi- Crystalline Tiling in Medieval Islamic Architecture, SCIENCE, Feb. 23
Text by Karen Weintraub, James Abundis / Globe Staff
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