Islamic tiles reveal sophisticated maths

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

[neverdem]

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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).

[BipolarBob]

They used to build magnificent structures. Now they blow up magnificent structures. Not what I would call progress.

[taxesareforever]

And from this was derived the Washington State WASL exam.

[WBL 1952]

Sorry, Muslim SLAVES use to design and build magnificent structures with the knowledge that the slaves had from their own foreign lands which was then claimed by the Muslims as their own.

[billbears]

bump. Thanks for posting this. Always amazes me to see how Islamic scientists and mathematicians expanded our understanding of science and how it passed on to the West. While current followers of Islam are not of the same cloth, it is interesting to see what they had to add in the past

[edcoil]

Muslims, or the Moors were excellent at construction. Muslims were not Islamic. They deteriorated to Islam in the 20th century and the middle east greatness was lost. That is the problem. they blame the west for the loss not their own culture and leaders.

[Fred Nerks]

http://www.freerepublic.com/focus/f-news/1789584/posts

Mediaeval Muslims made stunning math breakthrough
Scotsman ^ | 22-Feb-07 | Will Dunham


Posted on 02/22/2007 6:15:51 PM PST by xcamel

[goodnesswins]

ROFL...thanks for THAT laugh!

[ClearCase_guy]

Muslims were not Islamic. They deteriorated to Islam in the 20th century

Hello?

[neverdem]

Nature Insight: Skin Biology Nature has 6 free access articles from disease to tissue-engineered skin.

The Corn Threat

Studies to look into regrowing digits, limbs

FReepmail me if you want on or off my health and science ping list.

[isthisnickcool]

mohammad 1 has cut off two heads and has put them on a camel headed to mecca at 2 miles and hour. mohammad 2 has three heads strapped to his goat in medina. If both mohammads leave at the same time and at the same speed which one will blow himself up first?

[Andy from Beaverton]

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.

[tkathy]

Muslims have made no contributions to society other than hatred and death since then.

[uptoolate]

It depends, how many Westerners and Jews will each Mo pass?

[Fiddlstix]

Bingo!

[Ozone34]

I don't think so....
http://www.ninevehsoft.com/fiorina.htm

[a_Turk]

:))

[davisfh]

"mohammad 1 has cut off two heads and has put them on a camel headed to mecca at 2 miles and hour. mohammad 2 has three heads strapped to his goat in medina. If both mohammads leave at the same time and at the same speed which one will blow himself up first?"

I sense that you are as enthralled by this dubious subject as I am. The big question here is, what have these people contributed to mankind of late? Anyone out there want to answer that? Likely not in that the answer is already well known.

[PUGACHEV]

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.

[BipolarBob]

I never said we didn't owe a debt to the ancient Persian/Chaldean civilization. I was comparing then to now. Now we owe them fairness in trade and friendship IF they want it. If not let them go their way way, we go ours.