Mark Henderson, Science Editor
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Medieval Islamic artists produced intricate decorative patterns using geometrical techniques that were not understood by Western mathematics until the 20th century, scientists have discovered.
The combinations of ornate stars and polygons that have adorned mosques and palaces since the 15th century were created using a set of just five template tiles, which could generate patterns with a kind of symmetry that eluded formal mathematical description for another 500 years.
The discovery, by Peter Lu, of Harvard University, published in the journal Science, suggests that the Islamic artisans who created these typical girih designs had an intuitive understanding of highly complex mathematical concepts, even if they had not worked out the underlying theory. “We can’t say for sure what it means,” said Mr Lu, who is studying for a PhD in physics. “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. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we thought.”
Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines. It had been assumed that straightedge rulers and compasses were used to create them an exceptionally difficult process as each shape must be precisely drawn.
From the 15th century, however, some of these designs are symmetrical in a way known today as “quasicrystalline”. Such forms have either fivefold or tenfold rotational symmetry meaning they can be rotated to either five or ten positions that look the same and their patterns can be infinitely extended without repetition. The principles behind quasicrystalline symmetry were calculated by the mathemetician Roger Penrose in the 1970s, but it is now clear that Islamic artists were creating them more than 500 years earlier.
Mr Lu, who designs physics experiments for the International Space Station, began wondering whether there were quasicrystalline forms in Islamic art after seeing decagonal artworks in Uzbekistan, which he visited after a trip to a space facility in Turkmenistan.
On returning to Harvard, he started searching the university’s vast library of Islamic art for quasicrystalline designs. He found several, as well as architectural scrolls that contained the outlines of five polygon templates a ten-sided decagon, a hexagon, a pentagon, a rhombus and a bow-tie shape that can be combined and overlaid to create such patterns.
There is no evidence that the template tiles were themselves attached to surfaces to create mosaics. Artists probably used holes in the templates to trace a design on to a surface, which would be made into a mosaic.

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Perhaps one of the greatest books ever written was Henry Weaver's Mainstream of Human Progress which explains to perfection the intimate connection between economic prosperity and freedom-the essence being that when one is free, one naturally inclines himself towards advancing his wealth and circumstances through innovation, invention and good ol' fahion hard work. He writes glowingly of the first thousand years of Islam and their advances in all the higher fields of human endeavor-the arts, sciences, mathematics, poetry, etc.-which he clearly demonstrates was rooted in their rather laissez faire mentality towards the rights of individuals and their property as opposed to the modern statist idea that these things are mere robotic components for the machine they govern. Mathematical genius such as this, among other wondrous works of the Arab mind, when seen in its proper perspective, as Weaver portrays, should really come as no surprise to those who know their history.
Charles Torello, Dallas, Texas
Islam's contribution to "art, architecture, science, mathamatics, medicine, music, engineering, philosophy, literature or anything else of value" were halted by a number of factor. For Mr. Clement Knorr edification, I would say that a major reason for this faliure was the colonial occupation of Muslims by the Christians of the West. While the physical occupation gradually ended only in 1960s after over one hundred years of struggle by Muslims, West's economic colonialism continues unabated through overthrow of nationalist governments, military support of puppet non-democratic regimes throughout the Muslim World and military control over their natural resources. All this contribute, at least in part, to Muslims lagging the West. Mr. Knorr would take comfort from the fact that one thing that the Muslims did not contribute to the World over the last five hundred years was the concept of genocidal wars that some historian believe to be uniquely Western in origin which has helped it gain economic dominance over the rest of the world, including Muslims.
I Hyder, Cranbury, NJ
The accomplishments of Islamic civilization in Central Asia have been rich, but relatively unknown to the Westerners. While it is probably true that in the past 500 years or so it undergoes crisis in innovations, when living in Central Asia I came across various ingenious developments, and learnt that in 1929 Tashkent (Uzbekistan) was the site of a first experimental TV broadcast. I read there about various contemporary experimenmtal tests of medical drugs, one of them apparently successful against the skin cancer. On the balance, this is not much in comparison with the West, but it should remind us that to remain innovative is not given for granted.
Slawomir REDO, Vienna, Austria
Islam had a 500 year head start on the West in science and math. Then they collapsed. The intellectual squalor of Islam is it's own faulty choice.
Dennis Larkin, Omaha, KS, USA
Any doubter of Islam's accomplishments in the past need only visit the sublime Alhambra in Spain. That being said, will someone enlighten me as to what contributions they have made to art, architecture, science, mathamatics, medicine, music, engineering, philosophy, literature or anything else of value in the last five centuries?
Clement R Knorr, Tucson, Arizona,
As usual, no mention of India, where the Arabs learned everything they then used and spread into the West. Same as the Greeks and their metaphysics, etc. All from India. Every religion sprang from the eternal Vedas, as well.
hp, austin, tx
The article is pretty much on point. But I think make the mistake of confusing Arab culture withe Islamic culture. They are really two different things.
The Middle East became a cultural wasteland when the religion of the of the middle east became so stringent.
Eric, Gainesville,
The world owe the Muslims and Islam big time for their contribution to all the sciences and Humanity period.Any Yahoo who will contest this need only put aside the cap of arrogance and study the true unbiased history.
Truth be told, the muslims excelled in Hygiene and introduced the use of soap.
Undoubtedly, The Jews and Christians played a role because the Muslims did not exclude them from their research.Fact....The first university is Al Azhar in Cairo Egypt.The Jews and Christians studied there.And why not.
Islam teaches that we all came from one pair- adam and Eve, news flash-- we are brothers and sisters in humanity.
Let's stop fighting each other and cooperate for the good of Mankind.
Saeed Khan, Fla, Usa
The muslims took from those they conquered. Mainly the Jews and Christians. They were not particularly inventive, as their religion stifles new thought. Don't be so quick to praise them for all their technological advances, for the most part, it wasn't muslims who came up with the ideas, it was those they ruled.
read: The Politically Incorrect Guide to Islam and the Crusades.
Jim, Charleston, South Carolina / CSA
James
Don't be so paranoid. It's not hidden history. I learnt it at school while studying Greek. The debt we owe to the Islamic world in preserving (and extending) the work of the Greeks in mathematics and geometry (and much besides) has long been acknowledged.
Laky
Learn to use apostrophes if you want to be taken seriously (or indeed, understood at all)
John, Tokyo,
Why are you so surprised, what we have in the West now is mostly based on Islamic teachings from Spanish Muslims (Moors). Al-bruni, Ibn Khaldun, Kwarazimi, ibn Sina (Averroes), Ibn Rushd and many many more were great Islamic scientists, mathematicians, philosophers etc. This is hidden history. Medieval times were when Islamic sciences flourished but this history is not taught in the West to preserve the Islamophobic prejudices against Arab, Muslims and Islam. It is as if we jumped from the time of Jesus to 1942 and medieval times never existed! Western renaissance was based on the foundation of Islamic sciences.
For instance did you know a Muslim mathematician, called Al-Kindi was the first documented hacker? He wrote the first ever book on crypto-analysis circa 925 AD
If you want know what you missed checkout http://www.muslimheritage.com/
James Kramer, London, UK
If anyone's interested in having a look at how to generate Penrose tilings under Windows, I wrote the following for my University degree some time ago: http://www.stephencollins.net/web/penrose/
Stephen Collins, Stamford, USA
Mr Lu as lived a somewhat sheltered life, it seems.
I find information like that on google videos when researching islamic culture and history, in particular I remember one documentary by the BBC, it was very good.
You can find this kind of art work in Spain, its copied mostly, but it's learned and its still there. History!!
One thing I have come to find is that the human brain doesn't tend to reject mathematics.. I cant prove it, but its less common than what we class as ''illiterate'', someone who cant read and write?? Is that correct ..? Maybe something to think about.
Laky, Birmingham,
Show me a picture, please..
Ken Booker, Rochester, New York USA
that's great guys.
Thomas Magnum, London,