architecture: The Islamic World 81 Mathematics in Stone Architecture has sometimes been called “mathematics in stone.” An architect in any culture has to have a firm grasp of the principles of measurement, angles, the weights and carrying capacities of materials, and similar mathematical concepts This grasp of mathematics was nowhere more apparent than in medieval Islamic architecture, particularly in the elaborate and highly complex designs of tile work found in surviving medieval Islamic buildings Only in the 21st century have scientists come to appreciate fully the complex mathematics that may have been involved in the construction of this tile work Many of these scientists are crystallographers, or scientists who study the crystalline patterns of substances Using highly sophisticated instruments that measure the diffraction of light, they can examine in minute detail the form and arrangement of crystals and what are called quasicrystals While crystals are associated with glass or glasslike substances, quasicrystals are associated with such substances as aluminum, copper, cobalt, and nickel The prefix quasi- means “similar to” or “resembling.” A crystal is a symmetrical arrangement of atoms along three dimensions or axes The pattern can be repeated over and over, causing the crystal to grow and to fill up whatever space it occupies A quasicrystal exhibits the same structure of atoms, but instead of doing so along three axes, a quasicrystal exhibits the pattern along 10 Thus, quasicrystals are often referred to as decagonal quasicrystal structures, with the word decagonal deriving from the number 10 Only in 2007 did scientists discover that the crystalline structure of medieval Islamic tile work exhibits this decagonal quasicrystalline structure—a concept that was “discovered” by Western scientists only in the 1970s They use the term not to refer to the physics of the materials out of which the tiles were made but to refer to the symmetrical properties of the designs themselves Put differently, when they look at a sample of medieval Islamic tile work, what they see is a pattern that replicates the kind of crystalline pattern they would see in a substance under a microscope Clearly, such a pattern is complex beyond belief The question that arises is how medieval Islamic architects could have created these crystalline patterns to produce the breathtakingly beautiful tile work that adorns the mosques and other buildings they constructed To create simple geometric patterns, straightedges and compasses can be used But as patterns become more complex, it is inevitable that geometric distortion will occur, even when such tools are used If geometric distortion can take place with the simplest arrangement of tiles in a row, it seems almost inevitable that it would occur when the pattern becomes seemingly infinitely more complex However, scientists who have examined these patterns in Islamic tile work find virtually no distortion Thus, they conclude that the architects had not only an understanding of the complex geometry involved but also tools far more sophisticated than straightedges and compasses of architects in different areas of the Islamic world led to similarities in architectural designs and concepts throughout the region These architects began construction with delicate geometrical drawings as well as fragmentary drawings Masonry techniques included stonework, brickwork, clay walling, carpentry, plastering, and tiling Architects in the Islamic world also developed special types of construction, such as vaults, domes, and minarets Decoration and Ornamentation One of the characteristics of architecture in the Islamic world was the special treatment of decorations and the development of types of ornamentation that were not common outside Islamic territories The ornamentation in buildings, whether part of the structure or the exterior, was in contextual harmony with the spatial qualities of the architecture In other words, the components of decoration, as a complex overlay, not only formed surfaces but also defined spaces The prohibition of the use of sculptures and figural and animal art encouraged Muslim artists to find other techniques to decorate their buildings Taking advantage of the heritage from Mesopotamia, Persia, and to some extent Rome, early Muslim artists developed their decorations in three main phases In the first three centuries after Islam, patterns, repetition of elements, and intricacy in stone and stucco were applied as the main elements of decoration The second phase, developed mainly in eastern areas, created decorative effects through brick and terra-cotta patterns The most glorious age of this phase was the Seljuk Period (1038–1194), when ornamentation and structure were completely integrated in construction From the 10th century the decoration of portals and mihrabs became fashionable in