Maths on the domes : How geometric patterns were spiritually inspired in early Islam

May 8th, 2011 | By | Category: Art and Architecture, Featured Articles

Worshipping any other beings (e.g. humans or animals) apart from the One God was not permitted in Islam, and at the same time an anthropic form of the Almighty wasn’t allowed either. Such were the stipulations that led to an unusual form of art in the early phase of Islam, as it started reaching out from the Arabian peninsula.

Geometric design, Arabic calligraphy and flowers formed the three main themes of art in this phase, of which the geometric patterns formed the essential background to most architecture. What is most striking is the repeating pattern of these shapes, often incorporating extensive fractal dimensions of many fold symmetry. One cannot help feeling some deep underlying sense of pattern looking at today’s fractal images generated by computer algorithms, notably Mandelbrot and Julia sets. But as complex quadratic polynomials wasn’t part of Arab mathematics, the basic design conformed to Euclidean ideals in the beginning.

Section from the Topkapi Scroll, Istanbul, Turkey

The Topkapi scroll, from medieval Iran, a section from which is shown here, is perhaps the best preserved specimen of an Islamic complex pattern projected on the architect’s drawing board. Currently at the Ottoman museum at Istanbul in Turkey, the Topkapi palace, this section depicts the construction of quarter vaults, using a three dimension element called a muqarna., a three dimension design based on interposition of flat girihtiles widespread in the late medieval Islamic world. For a short video demonstrating the use of girih tiles,go here

The first known translation of Euclid’s Elements into Arabic by al Hajjaj during the Caliphate of Harun al-Rashid around 786 A.D. But how far Greek mathematics permeated into Arab art and culture in the early years is perhaps not fully understood. Arabic mathematicians, who were the most advanced in the world during this era, went way way beyond Greek mathematics which was essentially geometry based (more of that in a future article). But what Arabic philosophy developed through art was the way of metaphysical symbolism of geometrical expression to the underlying unity of all existence.

“Geometry enlightens the intellect and sets one’s mind right. All its proofs are very clear and orderly. It is hardly possible for errors to enter into geometric reasoning, because it is well arranged and orderly. Thus the mind that constantly applies itself to geometry is unlikely to fall into error….”

-Ibn Khaldun (1332-1406), historian, writer, Tunis

Science, art and theology is often said to mingle into one, in view of this immense fractalness witnessed on the domes and ceilings of mosques of the Abbasid period style and beyond. For the scientifically minded, quasi-crystalline complex Penrose patterns appeared in Islamic art five centuries before they appeared in Western science (1). “”It is hard to picture,” said Paul Steinhardt, Princeton physicist who coined the term quasi-crystals in the “and it’s hard for humans to process these patterns and interpret them.” (2)

But despite skepticism that the Islamic artists did not actually ‘use mathematics’ to design their creations, it clearly illustrates that complex patterns in the human creative domain can intuitively arise from simple actions inspired by faith or science or both. Aesthetics transcend categorizations of knowledge or analysis, and to the early Arabic Islamic designers, science, art and philosophy all mingled into one – for many of them, science, the natural world, geometry and art were all one, God’s will expressed through Creation.

The geometry of the Art forms was remarkably constant through out the Islamic world, and over the centuries become increasingly intricate as newer generations of designers strove to achieve newer perspectives. This unity was symbolic of a greater unity of the expanding Islamic empire of faith, but more importantly, it was part of the birth of Western mathematics, where Euclidean geometry was soon followed by trigonometry and geometric polynomials.

Who said that God did not have a creative hand in science ? Or, geometry for that matter ?


(1) Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture : Peter Lu, Paul Steinhardt. Science 23 February 2007: Vol. 315 no. 5815 pp. 1106-1110
(2) Medieval Mosques Illuminated by Math. Link :

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