From The Independent
By Steve Connor, Science Editor
Friday, 23 February 2007
The decorative tilework that adorns some medieval Islamic buildings has been found to use basic geometric shapes that form a complex and highly intricate tiling pattern which does not repeat itself.
In modern mathematics the principle of non-repeating patterns on a flat surface is known as quasicrystal geometry, and the most famous example is known as Penrose tiling, after the Oxford mathematician Roger Penrose, who was thought to have discovered it 30 years ago.
However, two American mathematicians believe that near-perfect quasicrystal geometry was used by Islamic scholars earlier than the 15th century to decorate the walls of important buildings.
Peter Lu, of Harvard University, and Paul Steinhardt, of Princeton University, said advanced quasicrystal geometry based on 10-sided shapes is seen in the tiling patterns of mosques and madrasas of the Middle East and central Asia, predating its discovery by Western mathematicians by 500 years.
“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,” said Mr Lu. “At the very least it shows us that a culture we often don’t credit enough was far more advanced than we thought before.”
Complete at the source
Earlier related Post: Math Behind Ancient Islamic Tile Patterns Decoded – Study supported in part by Harvards Aga Khan Program for Islamic Architecture
Ismailimail 
“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,” said Mr Lu. “At the very least it shows us that a culture we often don’t credit enough was far more advanced than we thought before.”
This post from Ismaili Mail’s Spirit and Life Blog also has some interesting information on how the fundamental principles of Mathematics thoroughly permeate Islamic Art and Architecture and, indeed, Allah’s creation itself, the Cosmos, all reflecting the abstraction of Allah the Transcendent and the monoreality of Tawhid:
http://spiritandlife.wordpress.com/2008/01/23/traces-of-the-calligrapher-islamic-calligraphy-in-practice/
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That isn’t the only thing in which Muslim Scientists were ahead of the West, usually without recognition in Western textbooks. Here is a post that has more information:
http://darvish.wordpress.com/2008/02/21/early-muslim-science-and-invention-teach-your-children/
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I was so glad to see Peter Lu’s articles about those five fold tilings from that high period of Islamic art. For me it does not diminish Roger Penrose’s findings, for Penrose has pushed the boundaries of the math of tiling patterns. Ammann tiles and other non-repeating patterns rediscovered what the Islamic artists had already found. The contribution that Penrose made with his tiles is that they are a minimal set of tiles (2) that force a non-repeating pattern. And then the discovery of quasi-periodic crystals! Very interesting stuff, considering that Penrose proved (mathematically) that if a crystal is to grow by adding tiles/molecules to the outside edge, the entire pattern/crystal plays a part, not just local rules/physical-forces.
Now we know the chronology – It’s Art first then Math, that opens the path to the further discovery of reality.
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this post has some very interesting information
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Members of the WordPress community who like to explore geometry may like to see the ancient examples on:
http://sarsen56.wordpress.com/solve-this/
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