Advanced geometry of Islamic art

Medieval Muslims made stunning math breakthrough

A study of medieval Islamic art has shown some of its geometric
patterns use principles established centuries later by modern
mathematicians.

Researchers in the US have found 15th Century examples that use the
concept of quasicrystalline geometry. This indicates intuitive
understanding of complex mathematical formulae, even if the artisans
had not worked out the underlying theory, the study says. The
discovery is published in the journal Science.

The research shows an important breakthrough had occurred in Islamic
mathematics and design by 1200. "It's absolutely stunning," Harvard's
Peter Lu said in an interview. "They made tilings that reflect
mathematics that were so sophisticated that we didn't figure it out
until the last 20 or 30 years."

The Islamic designs echo quasicrystalline geometry in that both use
symmetrical polygonal shapes to create patterns that can be extended
indefinitely. Until now, the conventional view was that the
complicated star-and-polygon patterns of Islamic design were conceived
as zigzagging lines drafted using straightedge rulers and compasses.
"You can go through and see the evolution of increasing geometric
sophistication. So they start out with simple patterns, and they get
more complex," Mr Lu added.

He became interested in the subject while travelling in Uzbekistan,
where he noticed a 16th Century Islamic building with decagonal motif
tiling. Mr Lu, who designs physics experiments for the International
Space Station, was in the region in order to visit a space facility in
Turkmenistan. Islamic art traditionally uses a mixture of
calligraphy, geometric and floral designs because of a prohibition on
the portrayal of the human form.

Story from BBC NEWS:
http://news.bbc.co.uk/go/pr/fr/-/2/hi/middle_east/6389157.stm

Story from Reuters:
http://www.reuters.com/article/scienceNews/idUSN2245118920070222?src=022

Medieval Islamic artisans developed a pattern-making process for designing ornate tiled surfaces that allowed them to produce sophisticated patterns not seen in the West until centuries later, a new study suggests. Many walls of medieval Islamic buildings have ornate geometric star-and-polygon, or “girih,” patterns, often overlaid with a zig-zagging network of lines. This undated picture shows an archway from the Darb-i Imam shrine, Isfahan, Iran ( built in 1453 ) with two overlapping girih patterns. REUTERS/handout/K. Dudley and M. Elliff.

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Medieval Islamic artisans developed a pattern-making process for designing ornate tiled surfaces that allowed them to produce sophisticated patterns not seen in the West until centuries later, a new study suggests. Many walls of medieval Islamic buildings have ornate geometric star-and-polygon, or “girih,” patterns, often overlaid with a zig-zagging network of lines. This undated picture shows an archway from the Darb-i Imam shrine, Isfahan, Iran (built in 1453 ) with two overlapping girih patterns. REUTERS/handout/K. Dudley and M. Elliff.