Sophisticated tiling in Medieval ME architecture

[turbo]

I found this quite interesting. Enjoy.

http://www.physics.harvard.edu/~plu/publications/Science_315_1106_2007.pdf

 

[Crosson]

Muslim artists discovered all 17 regular tilings of the plane, long before westerners proved that this exhausted the possibilities using their "Group theory".

 

[matt grime]

discovering 17 regular tilings is strictly distinct from showing that there are precisely 17 regular tilings.

 

[Crosson]

discovering 17 regular tilings is strictly distinct from showing that there are precisely 17 regular tilings.

Granted, but its not as if they coincendentally stopped at 17. A mosque in Delambre has 17 tilings, each one representing one of the symmetry groups.

The muslim artists had clearly convinced themselves, within their standards of proof, that there were exactly 17 regular tilings of the plane.

Granted their 'proof by example' is not acceptable by our standards, but that is a judgement issue of rigor, what is not in doubt is that they held it as a theorem in their day.

 

[CRGreathouse]

Granted their 'proof by example' is not acceptable by our standards, but that is a judgement issue of rigor, what is not in doubt is that they held it as a theorem in their day.

I, for one, doubt that they held it as a theorem.

 

[Crosson]

I, for one, doubt that they held it as a theorem.

Alright, I concede.

Consider the 'bridges of Konigsberg" problem, treated by Euler. I am sure that many people accepted that such a circuit was impossible who did not posess a proof. Because the problem of classifying plane tilings is more difficult then the Konigsberg bridge problem, I am impressed that these artists solved the problem in so far as they did.

 

[Doodle Bob]

btw, folks, there is an article in the NY Times about this as well today (2/27).

Incidentally, it is *unknown* how much the designers of these patterns knew about the mathematics involved. It is entirely possible that someone during the, oh, about 500 years of the Islamic middle ages derived what we would call a rigorous proof of the existence of the 17 regular tilings or of the quasicrystal tilings. One should always try to leave one's cultural biases at the door when exploring these types of topics. Our group-theoretical mechanics of proving the former may not be the only way.

What I'm curious, though, is why the physicists are getting all the press about this. Mathematicians -- particularly, mathematical educators -- have been utilizing Islamic tile patterns for decades both as research and as a method to teach geometrical thinking.