I don't know if this is true for all of Islam, but there is at least a subset of Muslims who do not include depictions of people, animals or plants in their art, based on their interpretation of a passage from the Quaran, which can be taken as forbidding it. While on one hand, this seems like a severe limitation on artistic expression, the practical result has been the development of absolutely beautiful alternative (i.e. "acceptable") art forms, particularly geometric mosaic tiles and tapestries. Much of the Muslim world is now decorated with these abstract designs and calligraphy, which have been refined to a dumbfounding degree complexity and stunning beauty. Achieving patterns like this requires a certain mastery of geometry- a recognition of how interlocking and recursive patterns can be arranged in an aesthetically pleasing manner. That's really what's at the heart of this book- the mathematics and geometry that supports this art. It is no coincidence that Islamic civilization gained mastery over abstract geometric patterns... one thousand years ago (about the time the strict limitations on artistic expression were first being implemented) the Muslim world was at the forefront of mathematics: developing algebra, plane geometry, the concept of zero, and the mathematic foundations of astronomy. A quick glance at the chapter titles should give you an idea of how in depth the text is, and how much mathematical discussion is involved with these patterns:Sixes ExtrapolatedTransforming a SubgridSix of One Three Times FourFurther Twelves Three-Fold PermuatationsFour-Fold PermutationsTen-Fold TilingPerfect FourteensDome GeometryI've got the idea that some of this is obscure or esoteric, just because Google images doesn't even have much of a selection for some of these terms, or if they do, it is non-Islamic. Yeah, I should mention that... even though this book is focused on Islamic art, the same principles show up in the much more recent art of M.C. Escherand traditional Celtic artso the book has something to offer fans of those, as well. Overall, the mathematics of this book was a bit beyond me, but I could put the pictures with the text to at least get a general idea of what the authors were getting at. I suspect other GoodReaders will likely get more out of it than I did; probably Manny and NGE, approaching it from the math perspective, and certainly Mon, coming from the artistic side. Still, for the pictures alone, I would say this inexpensive little volume is worthwhile to anybody who likes the images I've posted here.