Use of Geometry in Islamic Art

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Similar to most artistic styles and art movements, Islamic geometry “is interwoven with the history and cultural traditions of the region in which it flourished (Ateliers, 2013). While the Islamic faith dos not outright forbid the use of figural imagery, most interpretations of the Qur’an have discouraged the use of animal or human (including mythological or fictional) representations in art; and thus, it is excluded from religious settings (Victoria and Albert Museum). Thus, the use of geometry became a means of artistic expression that is often based on highly sophisticated geometric shapes and patterns, which are often reflective of religious ideas and objects in the natural world. Today, they can be seen as decorative elements on walls, ceilings, doors, minarets, domes, and clothing.

The use of geometric patterns in Islamic art can be traced back to rise of Islam during the 7th century (Abdullahi & bin Embi, 2013). During the 7th and 8th centuries, floral and vegetal patterns were most common. By the 9th century, simple and elementary geometric designs could be observed. For example, the Mosque of Ibn-Tulun demonstrates the use of 6- and 8-point geometrical patterns and it is one of the first accounts of woven geometric patterns in Islamic decorative art. One of the greatest movements came during the era of the Seljuks (1038-1194 CE), who made great efforts to transform their ornaments from floral to geometric decoration, often utilizing sophisticated patterns. With the introduction of highly complex and sophisticated patterns (e.g., 10-point and abstract 6- and 8-point geometrical patterns), this era marked a radical change in the application of conventional geometric patterns. The second artistic movement came with the Mamluks (1250-1517), who began to combine multiple types of patterns into single decorative arrangements. This period also marks the earliest signs of 10- and 16-point patterns. Modern Islamic art continues to use many of the same patterns, with the exception that advances in technology (e.g., computerized use of algorithms in graphic design) and various tools have made it easier to make more complex patterns and reproduce them faster.

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The most common geometric elements used in Islamic art are circles and interrelated circles, squares or four-sided polygons, star patterns (usually derived from squares and triangles inscribed in a circle), and multisided polygons (e.g., hexagons and octagons). There are two elements that appear most central to Islamic art: symmetry and tessellations. Sometimes one can observe a single line of reflective symmetry (usually from top to bottom) and other times there may be three or four (Victoria Albert Museum). Straight translations, rotational movements, as well as reflections can all be found in Islamic designs. These shapes are then combined, duplicated, and interlaced to form intricate patterns (Metropolitan Museum of Art). These patterns are often referred to as tessellations, in which regular polygons repeat to tile a surface plane. Only three types of regular polygons can tessellate (on their own) in a Euclidean plane (triangles, squares, and hexagons), which is referred to as “regular tessellation.” “Semi-regular tessellation” also follows a Euclidean plane, which is when several different regular polygons are combined to form the grid or pattern.

Those patterns that follow regular and semi-regular tessellations, by virtue of their design (e.g., shapes have equal lengths, angles, etc.), follow all five of Euclid’s postulates. However, not all Islamic art follows this type of pattern, so any designs that are left with spaces between shapes (that are not regular geometric shapes) or are random (e.g., don’t follow symmetry) could violate one or all of Euclid’s rules. Additionally, not all Islamic art is two-dimensional (e.g., architecture); thus, non-Euclidean forms of geometry (e.g., hyperbolic) may apply to those that are three-dimensional. In general, the mathematic pattern appears to be an integral part of the Islamic art. The repeating patterns give the illusion of infinity, reminding Muslims of the infinite nature of Allah. Numbers also seem to play a role in reflecting certain Islamic themes, such as using octagons to represent the eight angels that will bear the throne on The Day of Judgment. So, while the degree to which Islamic designs adhere to laws of geometry varies, it can be argued that some form is evident in every piece of Islamic art.

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