It is a beautiful object, that the "study's" authors attempted to turn into a religio-political statement, while inventing history.
At the same time, they admit there are flaws with their only "perfect" (the joys & wonders of modern education!) example, which in itself shows the lie of the 'mathematical discovery' aspect of it; else it would have been repeated, perfected, and applied in a growing, more general, and progressively sophisticated manner throughout Islamic art.
The entire "study" is just one more in the never ending series of the "greatness of Islamic science/math/technology/art" propaganda. It is not science, though it mimics some aspects of scientific study, so merits no exclusively serious 'discussion'.
This is a tile with repeating patterns on it, nothing more.
In point of fact, it is many thousands of tiles laid in a mosaic pattern, that just happens, while pleasing to the eye, demonstrates (almost) a mathematical principle discovered, and proved, many centuries later. It is like trying to state that Roman engineers understood modern engineering calculus, based on the surviving bridges or buildings that trial and error slowly evolved as safe, sturdy structures, while ignoring all the previous failed attempts; and without one shred of evidence of such sophisticated calculations.
Yes, we all know Islam is evil.
Sometimes, based on many (not yours!) posts I come across on FR, I'm not totally convinced of that. OTOH, these threads really are not the time & place for it.