Geometry and Islamic Art: Explorations of Number, Shape and the Nature of Space

Andri Handayani | CRCS | Workshop


xxTalking about Islamic art and geometry cannot be separated from the classical Greek author and  mathematician, Euclid, whose works were translated into Arabic and whom then Muslim mathematicians advanced his understanding in math and geometry and translated the entire Greek corpus and transmitted great corpus of mathematics to the European worlds. In West and Northern America, we know that the math has roots from the classical Islamic world and back to Greek antiquity. In education, we know Arabic number, rooted from India, now we call that Hindu-Arabic numbers. Euclid formerly was fundamental to the training of geometry in elementary, junior and senior high schools. Today, Euclid is being eliminated from the curriculum with much greater emphasis on numerical and symbolic formulation which is very different from mathematical approach and understanding than Euclid’s.Those statements were explained by Carol Bier, the visiting scholar in the Center for Islamic Studies, Graduate Theological Union, Berkeley, USA opening a workshop entitled Geometry and Islamic Art: Explorations of Number, Shape and the Nature of Space hosted by Indonesian Consortium for Religious Studies (ICRS) UGM on July 12, 2013 at UGM Graduate School.


In this workshop Carol Bier not only presented the geometry and Islamic arts but also gave some exercises about geometry to the participants. In the first exercise, she gave paper plates to the participants and asked the participants to put two dots anywhere within the circumference of the paper plate. After putting the dots, the participants were asked to fold the paper plate so the dots touch each other. Surprisingly, the result from all participants is the same, a semi-circle or half circle. Why? According to Carol if we connect the points and draw a perpendicular, then the perpendicular will always be the diameter. Each point when we connect them we write the diameter, the result will always be the same. The heart of geometry and Islamic arts basically focuses on circle and its center.


Carol Bier conveyed that a country has particular pattern or shape in daily life. While Japanese are familiar with circle and rectangle seen from the way they cook sushi, Indonesian people are familiar with triangle pattern and shape. It was proven when she invited the participants to fold a gold paper into half. Most participants folded it into a triangle. Carol exemplified the triangle patterns in Indonesia can be seen in the decoration of gate in Soekarno-Hatta Airport and the batik pattern. One participant also said that the folded handkerchief in the funeral is also the example of triangle shape in Indonesia.


She also described the connection between shape, pattern and arithmetic. The activity of folding a square into rectangle or into triangle over and over again resulted 16 smaller squares. It is closely related with arithmetic formulation specifically quadrat multiplication, subtraction and square root. It is basic and fundamental principle of the relationship numbers to the special dimension. “And that is a basic number fact that underlies so much of Islamic arts,” Carol said.


Carol continued that large tradition of Islamic arts spread all the way from Spain, North Africa, Indonesia, Arabic land, Andalusia, Iraq, Middle East, India, Samarkand, Central Asia, West China, Central Africa, Mozambique and Madagascar. One of Islamic scholars who focused much on geometry was Nasir al-Din al-Tusi. She also mentioned two famous buildings with geometric pattern namely Al Hambra, Spain and Taj Mahal, in Agra, India. “The geometric patterns are not only found in 2 dimension but also 3 dimension, implemented in ceramics, woods, division of dome structure divided through application of geometry, arches, minarets, strict symmetric layout of garden and pool. All of the patterns we seen so far ultimately come back not only division of square, but also geometry of circle and center,” Carol explained.


Euclid’s works were translated in Arabic by Nasir al-Din al-Tusi. She also said that the first scholar Al Khwarizmi (9th century) in Bagdad, wrote al-jabr wa’l-muqabala. He is one who established algebra. There is no Latin word algebra. Khwarizmi also became the source for the Latin Algorithm. His algebra worked with coin establishing his problem by laying out the dirham. Dirham at that time had stars and crescents in 4 sides which had close relationship with textile 8th century of Emperor Shomu in Japan that was clearly influenced by Hindu temple of Indonesia. It can be seen from the floor pattern in Borobudur.


After explaining, Carol also gave other exercises on making 6 and 8 pointed stars from folding and cutting a circle paper. It was amazing that without measurement, we can create a beautiful pattern. Actually no measurement is fundamental geometry. “The gamelan music is intimately each instrument related to the circle in time. The gamelan musicians are getting ready to jump into the natural geometry of nature that exists. The geometry exists in nature,” explained the former textile curator of Textile Museum of Washington DC.


According to Carol the geometry is inherent in the circle. This not only underlies Islamic patterns and arts but also underlies the theology of Ibn ‘Arabi. He introduces two names of God outside Asmaul Husna, Al Mukhid (the circumference) and Al Mukhtab (the center). What could be in circumference and the center is nothing but God. The theology that incorporates the principle of relationship between number, space and the nature of shape or number, shape and the nature of space into a theology that articulates at the theological dimension what we have been explained. “I haven’t found Islamic thinker before Ibn ‘Arabi who has articulated it so fully,” Carol said.



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