It honours nature in an abstract decorative art, and benefits through its lack of restriction by the constraints of a numerical system.
A brief introduction to the history of Arabic or Islamic geometry is set out on the next page together with methods by which those geometries can be readily constructed using the traditional means of a straight edge and a pair of compasses.
But having said that, I believe it would be useful to begin this page with a note on the understanding we in the West have of Arabic or, perhaps more accurately, Islamic geometrical design as it is a wide field of study and there are many misconceptions about its origins, interpretation and character.
However, the example is not from Arabia but was made in France and is one of a pair of silver door panels, shown above on its side.
At its simplest, Arab scholarship enlarged our comprehension of underlying geometries, and Muslim craftsmen, not all of them Arabs, relied on this body of knowledge in producing their characteristic fields of tiles, mosaic, plaster and wooden patterns that were applied to elements of their buildings.
Generally they are seen as two-dimensional surface treatments, though there are examples of three-dimensional work in many areas of the Islamic world, particularly with the .
While many of the designs illustrated here, including my attempts to deconstruct them, are based on two-dimensional designs, there are many examples of three-dimensional design work in the Islamic world.
Here to the side is the top of a fifteenth century wooden Egyptian that has been articulated with pendentives, a form of cantilever that is commonly used in masonry constructions, though here is more decorative than structural due to the inherent character of timber which has both compressive and tensile qualities which stone lacks.
Based this time on twelve-point geometry rather than the eight-point shown above, there is an evident family feel to the design of the two panels, one that is familiar to many people as characterising their recognition of Arabic or Islamic design.