Islamic mosaic and geometry

The term ‘mosaic’ usually refers to a decorative art form where the image (two dimensional, flat or curved) is constructed using small coloured pieces of glass, stone, tile, ceramics, or some other material. In the context of this exposition, we adopt a somewhat narrow, but more appropriate meaning. We think of a mosaic as a decorative or art form where a certain recognizable pattern (sometimes called a matrix) is repeated in two dimensions. The important part of the definition is the requirement that the iterations of the pattern occur in two dimensions i.e., in two distinct directions, such as horizontal and vertical.

Formalizing this intuitive idea of a mosaic, we obtain the corresponding mathematical concept: a tiling. To form a tiling means to cover a plane with various geometric forms (such as polygons or shapes bounded by curves – so-called ‘tiles’) in a way that leaves no gaps (the whole plane is covered) and does not allow for overlaps (the tiles cannot be partially of fully placed on top of each other). Sometimes the word ‘tesellation’ is used in lieu of ‘tiling.’

We think of mosaics in the way they were meant to be viewed and thought about – as infinite extensions of the pattern that is actually shown. Being exposed to a small part, we contemplate the whole. The word ‘plane’ in the mathematical definition represents that two-dimensionals, unbounded surface where the mosaic extends (‘unfolds’).

Although mosaics can be identified among the artifacts created by people in almost every culture, past or present, nobody has designed and used them with the skill, knowledge and sophistication of the artisans and artist working in the Islamic World (mostly between 10th and 16th centuries AD). The key of our understanding of this phenomenom lies, perhaps not surprisingly, in geometry.

There are several reasons why geometry played and important role in the Islamic world. First of all, geometric forms, patterns and configurations provided a desired level of abstraction. Islam being a non-figurative religion, its theologians selected geometry as a medium of conveying images of God.

Secondly, geometry was viewed as a force capable of unifying the domains of the secular and the religious: ‘the study of sensible geometry leads to skill in all practical arts, while the study of intelligible geometry leads to skill intellectual arts because this science is one of the gates through wich we move to the knowledge of the essence of the soul, and that is the root of all knowledge.’ (From the treatise Rasai ’il, by scholars belonging to the Ikhwan Al-Safa or Brotherhood of Purity. 9th and 10th centuries AD.).

Finally, intricate knowledge of properties of geometric objects (such as lines and circles) and sophisticated computational skills became essential for the development of astronomy. Accurate astronomical observations were employed in the production of almanacs and calendars, for time-keeping, and as a tool of navigation (at sea, and on land, especially in large deserts).

Geometric patterns can be found, in Islamic world, virtually everywhere: in tile mosaics, friezes and other wall ornaments, arabesques, coffered ceilings, floors, carpets, manuscripts, wooden carvings, doors, screens, executed in a variety of media (tiles, bricks, marble, wood, brass, paper, plaster, glass, etc.).