Medieval Islamic Architecture Presages 20th-century Mathematics
(on picture - Mosque of Sheikh Lotfallah, Isfahan, Iran)
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.
"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 toolkit 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;
madrasas 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.
Note: This story has been adapted from a news release
issued by Harvard University.
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