Islamic tiles reveal sophisticated maths

news@nature.com ^ | 22 February 2007 | Philip Ball

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Published online: 22 February 2007; | doi:10.1038/news070219-9

Islamic tiles reveal sophisticated maths

Muslim artists were 500 years ahead of western researchers.

Philip Ball

The pattern on the Darb-i Imam shrine, built in 1453, is almost identical to Penrose tilings, discovered in 1973. Click here for a larger image K. Dudley and M. Elliff

The complex geometrical designs used centuries ago in Islamic art and architecture were planned with a tiling system that was not discovered in the West until five centuries later, two physicists have claimed.

Islamic tiling patterns were put together not with a compass and ruler, as previously assumed, but by tessellating five different tiles with complex shapes, say Peter J. Lu of Harvard University in Cambridge, Massachusetts and Paul Steinhardt of Princeton University in New Jersey.

The researchers think that this technique was developed around the start of the thirteenth century. By the fifteenth century, it was sophisticated enough to make complex patterns now described as quasi-periodic.

These patterns were 'discovered' in 1973 by the British mathematical physicist Roger Penrose. In 1984, they were found in natural substances called quasi-crystals that seemed to break the geometric rules of atomic packing.

Perplexing patterns

The patterns in question are called girih. They consist of polygon and star shapes interlaced with zigzag lines.

Writing in this week's Science¹, Lu and Steinhardt propose that girih were produced from permutations of a handful of shapes ranging from pentagons to bow-ties. These tiles could be drawn with compasses that were known to medieval Islamic mathematicians.

Reconstruction of the tiling on the Darb-i Imam shrine. Click here for a larger image Peter J. Lu

Scrolls by Islamic artists to explain their methods show tiles with these shapes, confirming that they were used as conceptual building blocks. Lu has found no evidence that the tiles were actually made. "But we speculate they were," he says, "so as to be used as templates in laying out the actual tiling on the side of a building."

"Once you have the tiles, you can make complicated patterns, even quasi-crystalline ones, by following a few simple rules," he adds.

Quasicrystals show five-, ten-, and twelve-fold symmetries, in which they can be superimposed on themselves by rotating them by a fifth, tenth or twelfth of a full circle.

But this seemed to violate the rules of geometry. Polygons with five, ten and twelve sides cannot be packed together without leaving gaps — unlike, say, the hexagons in a honeycomb. Steinhardt solved the problem by showing that Penrose's tiling scheme could generate quasi-crystalline patterns.

A girih design on the Darb-i-Imam shrine in Isfahan, Iran, which was made in 1453, is almost identical to a Penrose tiling. One of the pattern's mesmerizing features is that, like a true quasi-crystal, it looks regular but never repeats exactly.

"I'd conjecture that this was quite deliberate", says Lu. "They wanted to extend the pattern without it repeating. Although they were probably unaware of the mathematical properties and consequences of the construction rule they devised, they did end up with something that would lead to what we understand today to be a quasi-crystal."

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References

1. Lu P. J. & Steinhardt P. J.. Science, 315 . 1106 - 1110 (2007).

[PA Engineer]

"Islamic tiles reveal sophisticated mayths"

Better.

[ModelBreaker]

Now we owe them fairness in trade and friendship IF they want it. If not let them go their way way, we go ours.

Agree with your first sentence. But there's no evidence the second one will work. "Their way" seems to involve a bunch of them coming to my fair city, asking for special rules that apply only to them, and then, when they don't get their way, blowing up a portion of my city. Eventually, they will ask my grandchildren to convert or die. Doesn't work for me.

[BipolarBob]

If not let them go their way way, we go ours.

I did not elaborate on the enforcement of the they go their way. If they do NOT go their way we send them to the 72 Virginian place with extreme prejudice.

[FairOpinion]

ping

[SunkenCiv]

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A fool lies here who tried to hustle the East (Kipling) barfarama
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[SunkenCiv]

Thanks Fairopinion.

To all -- please ping me to other topics which are appropriate for the GGG list. Thanks.

Please FREEPMAIL me if you want on or off the
"Gods, Graves, Glyphs" PING list or GGG weekly digest
-- Archaeology/Anthropology/Ancient Cultures/Artifacts/Antiquities, etc.
Gods, Graves, Glyphs (alpha order)

[Fred Nerks]

You really do need to read this: (All of it)

http://www.americanthinker.com/2005/08/the_notsogolden_age_of_islamic.html

final paragraph:

Why should we care that dhimmi history has convinced most educated people that Christians lost Aristotle and Muslims restored him to them? Why should we care that they believe in a Golden Age of Islamic philosophy that never occurred? We should care because we should care about the truth, but more than that, because these false beliefs are actually quite dangerous, for in the malignant minds of terrorists, they justify murder. Dhimmi history confirms the sense of superiority Islamofascists feel, it sympathizes with their wounded vanity, it shares their enemies, it reminds them of their past glories, it makes them feel unappreciated, it flatters them, it makes them suspect treachery, and it tells them that they are right.

Dhimmi history has the disastrous effect of heightening the 'sense of injur'd merit' that the jihadists feel—along with Milton's Satan. The lies of dhimmi scholars are, like the borders of Islam, bloody.

[xcamel]

I posted a link to this on the other thread.. (#287)
http://www.freerepublic.com/focus/f-news/1789584/posts

[xcamel]

Look here too:
http://www.sciencenews.org/articles/20070224/mathtrek.asp

[aristotleman]

-----I'm tired of everyone thinking muslims are so smart. When did they start to make these advances given to them? When they conquered other nations.----- Andy from Beaverton


Your statement is not really true. Although much knowledge was assimilated when nations were conquered, there have been quite a few brilliant minds over there.

[xcamel]

And.. other than the thinly bigoted remark, they had free access to use and contribute to the legendary "Library of Alexandria" before it was burned, and wealth of knowledge lost there was incalculable.

[Sam Ketcham]

Very sophisticated math... 1 Bomb + 1 Bomb = 2 Boom or 1 Big Boom

[SunkenCiv]

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[MrsEmmaPeel]

We owe a great debt to Islamic culture because, ironically, it alone preserved the wisdom of the ancient Greeks at a time when the Catholic church considered such learning heresy.

What have you been smoking? Ever heard of the Library of Alexandria - the greatest repository of knowledge in the western world, destroyed by the MUSLIM conquest of 642 AD