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"We're finding widespread evidence for the same approach being used
for 500 years across the Islamic world," says Peter J. Lu, a graduate student
in physics. "Again and again, girih tiles provide logical explanations for
complicated designs."
Staff photo Stephanie Mitchell/Harvard News Office
Medieval Islamic architecture presages 20th century mathematics Peter Lu
finds advanced geometry in 15th century tilings By David Baron
FAS Communications
Intricate decorative tilework found in medieval architecture across the
Islamic world appears to exhibit advanced decagonal quasicrystal geometry - a
concept discovered by Western mathematicians and physicists only in the 1970s
and 1980s. If so, medieval Islamic application of this geometry would predate
Western mastery by at least half a millennium.
The finding, by Peter J. Lu at Harvard University and Paul J. Steinhardt at
Princeton University, will be published this week in the journal Science.
"We can't say for sure what it means," says Lu, a graduate student in physics
at Harvard's Graduate School of Arts and Sciences. "It could be proof of a
major role of mathematics in medieval Islamic art or it could have been just a
way for artisans to construct their art more easily. It would be incredible if
it were all coincidence, though. At the very least, it shows us a culture that
we often don't credit enough was far more advanced than we ever thought
before."
Breathtakingly elaborate geometric tiling is a distinctive feature of
medieval Islamic architecture throughout the Middle East and Central Asia. Art
historians have long assumed that simpler elements of the patterns were created
with elementary tools such as straightedges and compasses. But there has been
no explanation for how artists and architects could have created the
unmistakably complex tile patterns adorning many medieval Islamic edifices.
Peter J. Lu with his cousin, Christina Tam. The two traveled to
Bukhara, Uzbekistan, where Lu saw this tiling. 'It was the one that first
caused me to get curious about the whole issue of decagonal geometry in Islamic
patterns.'
Photo courtesy of Peter J. Lu
"Straightedges and compasses work fine for the recurring symmetries of the
simplest patterns we see," Lu says, "but it probably required far more powerful
tools to fully explain the elaborate tilings with decagonal symmetry."
While it's possible to create these patterns individually with basic tools,
they are incredibly difficult to replicate on a larger scale without generating
extensive geometric distortions. The most complex medieval Islamic tilings have
little such distortion, leading Lu to believe more is at play.
"Individually placing and drafting hundreds of decagons with a straightedge
would have been exceedingly cumbersome," Lu says. "It's much more likely these
artisans used particular tiles that we've found by decomposing the artwork."
These tiles, dubbed "girih tiles" by Lu and Steinhardt, consist of sets of
five contiguous polygons (a decagon, pentagon, diamond, bowtie, and hexagon),
each with a unique decorative line pattern. For medieval Islamic artisans, they
may have represented a tool kit for generating huge numbers of distinctive tile
patterns without the lengthy, painstaking, and often flawed process of creating
each line segment individually.
These girih tiles may have been used to generate a wide range of complex
tiling patterns on major buildings from medieval Islam, including mosques in
Isfahan, Iran, and Bursa, Turkey; madrassas in Baghdad; and shrines in Herat,
Afghanistan, and Agra, India.
In some cases, Lu found girih tiles used to create patterns of two distinct
scales on medieval Islamic buildings. This approach generates infinite patterns
with decagonal symmetry that never repeats - also known as a quasicrystalline
tiling, a phenomenon first described in the West in the 1970s by famed British
mathematician Roger Penrose and more fully explained by Steinhardt and Dov
Levine over the past 30 years.
In addition to examples on medieval structures that are still standing, Lu
has been able to match his girih tiles with drawings in 15th century Persian
scrolls drafted by master architects to document their techniques.
"We're finding widespread evidence for the same approach being used for 500
years across the Islamic world," Lu says. "Again and again, girih tiles provide
logical explanations for complicated designs."
Lu and Steinhardt's tile study was supported in part by Harvard's Aga Khan
Program for Islamic Architecture and by C. and F. Lu.
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