Geometry: Drawing from the Islamic Tradition

Getting students involved in careful observation and analysis and encouraging their exploration of cultural forms of expression is an excellent means of introducing mathematical ideas. Geometric patterns abound in Islamic art and architecture. Exhibiting great ingenuity over the centuries, Muslim artists and craftsmen created beautiful patterns to adorn architectural monuments and exquisite objects. The Alhambra in Spain and the Taj Mahal in India offer the most famous examples of extraordinary patterns using brick and glazed tile, or carved and inlaid marble. Other examples of patterns are made using metal, wood, and fiber. Students may gain conceptual and theoretical understanding of patterns through activities and hands-on exercises that relate circles to centers, axes and grids, symmetry and tessellations. Through folding and cutting, drawing and coloring, one learns about relationships among number, shape, and the nature of space, which so characterize geometric patterns seen in Islamic architecture, silk textiles, illuminated manuscripts, wood inlaid with mother-of-pearl, carved stone, and other materials, contributing to a beauty of form, pattern, and structure. Introduction Properties of the circle are fundamental to geometry. Circles and their centers underlie the formation of many geometric patterns in Islamic art across time and space from Spain in the west to India and the east, north into Central Asia and south of the Sahara in Africa. Not only in historic monuments, geometric patterns are also characteristic of Islamic art today around the globe where such patterns at times serve as cultural markers. Depending on location, students can take local walks, or they may use postcards or digital images to serve as a basis for analysis, or color line drawings to gain an understanding of two-dimensional patterns, which are based on points, lines, and angles in the plane. Whatever the activity, careful observation, reflection, and analysis draw students into geometry in an manner that is experiential and memorable, and may also instill an awareness of cultural issues and sensitivity. Sources to Study Islamic Geometric Patterns Print resources (see References: Books and Articles, below) provide numerous photographs of Islamic geometric patterns, and some include diagrams and analyses, along with discussion (Critchlow 1976; El-Said and Parman 1976; El-Said 1993; Broug 2013). Websites and online databases offer easy access to images (see References: On-Line Resources, below). Islamic geometric patterns abound on historic monuments in many locations, including Cordoba and Granada in Spain, Fez and Casablanca in Morocco, Cairo in Egypt, Damascus and Aleppo in Syria, Istanbul and Konya in Turkey, Bukhara and Samarkand in Uzbekistan, Kabul and Ghazna in Afghanistan, Ahmedabad and Delhi in India, Kuala Lampur in Malaysia, to name only some cities and towns. There are many more, as well as monuments in Islamic style throughout Europe, UK, and North America, and architecture in South and Central America in which Islamic influence is present. Add to this range of opportunities the rich collections of Islamic art in major museums throughout the world (see References: Museum Collections, below), which provide many examples of small scale Islamic geometric patterns to view up close, some so tiny they benefit from the use of a magnifying glass! Cultural Forms of Expression Although geometry in Islamic art is far too often portrayed as a response to a presumed prohibition against figural imagery, this is not borne out by the historical evidence of pictorial narratives that exist in book illustrations and miniature paintings, wall paintings and story cloths, coins, metalwork, and ceramics. (See, for example, Freedberg 1989). The predilection for geometric patterning is likely the result of intensive explorations into the nature of twoand three-dimensional space that comprised scientific endeavors supported by royal and princely patronage in both mathematics and architecture. The misunderstanding of Western perceptions may be linked to the 19-century promotion of Islamic geometric patterns as decorative and ornamental, without regard for cultural origins (Jones 1856). Historically, such patterns have deep cultural roots as emergent forms of visual expression in architecture and the arts in many media. They fit within a larger rubric that one might call “Post-Euclidean mathematics,” which includes, for example, advances in the development of algebra, trigonometry, spherical geometry, number theory, and algebraic geometry. Islamic Geometric Patterns: Activities and Exercises Four simple sets of exercises serve as an easy way to draw students into the world of Islamic geometric patterns, providing opportunities for experiential learning while sharing cultural values and introducing basic principles of geometry. 1. Establishing Grids The first exercise challenges students to tight-pack pennies (or any round coins of equal dimension). The pennies will tight-pack in only two ways – one yields centers that when connected form a square grid; one yields centers that connect to form a triangular grid. Ask students to compare the spaces of the interstitial areas between the pennies, to determine which is the tighter packing. Islamic geometric patterns are often derived from a grid generated by connecting the centers of tight-packed circles.