Medieval Islamic tilers

During his time working as a PhD student in Harvard University's Physics department Peter J. Lu realised there was a link between medieval Islamic tilers and a discovery by the mathematician Roger Penrose in the 1970s. An article in the New Scientist magazine, dated 3rd March 2007 explained that this meant Islamic tilers were hundreds of years ahead of their time.

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MEDIEVAL Islamic tilers, long renowned for the beauty of their designs,


Working with only a straight edge and compasses, they managed to create intricate geometric patterns


They did it, says Peter J. Lu of Harvard University,


Such patterns were thought to be impossible


It seems that medieval architects got there


Lu recognised the patterns


Islamic architects used tiles known as girih, often of thick and thin rhomboids,


It was these patterns that Penrose would later explain


Penrose himself was aware that his eponymous tiles


It was his suggestion that the patterns could be used

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were very similar to Islamic patterns.

somewhat earlier!

to create complex patterns such as those seen in the Darb-i Imam shrine in Isfahan, Iran.

that wouldn't be understood by western mathematicians for at least 500 years.

now seem to have been even more skilled than we appreciated.

until the mathematician Roger Penrose showed how to make them in the 1970s.

mathematically.

because they understood Penrose tiles.

to redecorate mosques damaged by the Iraqi invasion of Kuwait in 1990.

on a visit to Uzbekistan.

Penrose tiles

Classic Penrose tiles consist of two rhombi with angles 72 and 36 degrees.

The edges of the rhombi are all of equal length.
classic Penrose tiles
If you follow a few strict rules about how to place them together, you'll wind up with (= end up with) an aperiodic pattern. This means that no section of the pattern will be repeated as a unit.

 

Penrose tiling

"Now that I am able to visualize five-dimensional space in my head, I've noticed that I get a lot of weird looks from priests and small children." Roger Penrose, Oxford University mathematician

Penrose tiling

To see the archway from the Darb-i Imam shrine in Isfahan, Iran


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