Do you know "girih"? It is intricate patterns covered Islamic mosques in Middle Ages. It was assumed that the patterns were created using a compass and a straightedge, but now it seems that ancient Muslims may have stumbled on some advanced geometry, not discovered in the Western world until 500 years later. This is an article by physicists from Harvard and Princeton in 2007. They say that you can make intricate patterns by just five different shapes of tiles.