Five Centuries Ahead of the West
In Bukhara, so many people astonished by the beauty and complex geometry in the tiling in Abdullah Khan madrasah.
Dr. Lu (Harvard) and Dr. Steinhardt (Princeton) state that Islamic designers had mastered techniques 'to construct nearly perfect quasicrystalline Penrose patterns, five centuries before their discovery in the West.'
Dr Lu with his cousin in Bukhara, where he saw this tiling. 'It was the one that first caused me to get curious about the whole issue of decagonal geometry in Islamic patterns.' Photo courtesy of Peter J. Lu
'This would be a hitherto undiscovered episode in the spectacular developments of geometry in central Islamic lands...achieved by artisans probably inspired by theoretical mathematicians', said Islamic art specialist Oleg Grabar.
Esfahan nesf-jahan (Esfahan is half the world)
Sheikh Lutfallah Mosque, Esfahan, (1602-1619) built much later than the Bukhara mosque above. Architect: Muhammad Reza ibn Ustad Isfahani. Photo by Tile Driessen
Above, another view of Lutfallah by Mahdi Asheghvatan
Photo by Dietrich Meyer, above.
‘The study of sensible [i.e. of the senses] geometry leads to skill in all the practical arts, while the study of intelligible geometry leads to skill in the intellectual arts, because this science is one of the gates through which we move to the knowledge of the essence of the soul, and that is the root of all knowledge.’ The Rasai’il ikhwan as-safa (Encyclopedia of the Brethren of Purity, a vast compendium of knowledge compiled c. 950 CE.)
Another sample of what geometer-artists can do!
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| Praying room Nasr molk Mosque, shiraz-fars, Iran. |
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| Praying room Nasr molk Mosque, shiraz-fars, Iran. |
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| Bright colors combined with natural light. |
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| Multi colors-Muslim praying room, Mosque. |
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| Full of details, complicated, and seem harmony. |
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| Praying room. Feel personally, just between Me and God. |
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Combination of unique calligraphy (and The Arabic is the best Calligraphy in the world !),
geometric design, soft and natural colors creating this artwork looks more luxurious. |
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Combination of calligraphy and geometric design. Soft and natural colors.
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| Ceiling work. Hasan Mosque, Morocco. |
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| The sun lights comes in variety of beautiful colors. |
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| Colored Window |
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| Old Woman. Dzikr fervently. |
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| There's a Garden there... |
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| Ceiling brown. Like circular movement. |
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| Light through interior -400 years old minarets, mosque. |
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| Looking at people praying from star. |
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| Lotfollah Mosque, Ishafan, Iran. |
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| Toward main praying room, Mosque-Iran. |
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| King Hasan II Mosque |
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| The natural lighting has developed since mediavel IslamicArchitecture. |
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| Praying Fervently alone : "Just between Me and Allah." |
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| Mimbar for Preaching |
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| Reflections in Mosque floor. |
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| Inside Blue Mosque, red carpet lights |
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| Praying Jamaah inside one of Pakistan Mosque. |
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| Inside Dome of Kubah Emas Mosque, Depok, West Java-Indonesia. There's a cloud over there. |
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| Vault Nasr Molk Mosque-Shiraz |
Analysing Patterns
Above, Darb-i Imam shrine in Iran. Courtesy of K. Dudley and M. Elliff
A computer reconstruction of the quasicrystalline patterns shown above, courtesy of Peter J. Lu
Above, further analysis
Pattern from a Turkish mausoleum, c. 1200 C.E, above A reconstruction of the tile templates is overlaid at the bottom.
These tiles may have been used to generate a wide range of complex tiling patterns on medieval buildings, including mosques in Isfahan, Iran, and Bursa, Turkey; madrasahs in Baghdad; and shrines in Herat, Afghanistan, and Agra, India. This approach produces infinite patterns with decagonal symmetry that never repeat. (Harvard University Gazette)
Photo from Professor N. Rabat, above, Aga Khan Program at MIT
Photo by Nima Mehrabany, above
Penrose Tiling in Architecture
Algebra, a mathematical discipline that is independent of geometry and arithmetic which established by a Muslim Mathematician, Muhammad ibn Musa al-Khwarizmi (c. 780-850) that wrote "The Compendious on Calculation by Completion and Balancing, the first mathematician" (Al-Khwarizmi's al-Kitab al-muhtasar fi hisab algabr wa-l-muqabala) give roots to the mathematical development on next century, clearly influence directly how Muslim architecture developed. Then Johannes Kepler (1571-1630) used to explore non-repeating symmetries. The same concept that Sir Roger Penrose described in 1970s the mathematics of interlocking polygons whose pattern never repeats: quasicrystal geometry. "It shows us a culture that we often don't credit enough was far more advanced than we ever thought," said Peter Lu. “They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years.”
Penrose tiling is made of just two kinds of tiles, kites and darts. A kite is made from two acute golden triangles and a dart from two obtuse golden triangles.
The ratio of kites to darts is the Golden Ratio. The fact that the ratio is irrational is the underlying principle in the proof that the tiling is non-periodic, since the ratio would be rational in a periodic tiling. (With some notable exceptions, many European mathematicians did not recognise irrational numbers until the 19th century)
Because aperiodic (non-repeating) tiling is more challenging to design and install than ordinary repeating tiles, we seldom see it in modern buildings.
Properties of Penrose Tiling
Penrose Tiling is extraordinarily dense. It has a number of remarkable properties. One is that every finite portion of any tiling is contained infinitely often in every other tiling. Therefore, no finite portion of tiles can determine the rest of the tiling, and it is impossible to tell from any patch of tile which tiling it is on.
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| Tile Detail, UEA Mosque, Dubai. |
Architectural Scrolls
Until Peter Lu announced his findings to Western audiences, it was widely believed that medieval artists and architects were limited to the basic compass and straightedge. It is now known that the intricate accuracy of these designs is impossible with only compass and straightedge.
Professional mathematicians and master architects wrote architectural scrolls, important instructional manuals of the day, which were disseminated throughout the Islamic world. Inventive architects and artists kept improving the sophistication of their work until, by 1453, they achieved the quasicrystal.
Above photo by Mehrdad Tadjdini
‘This cannot be solved with plane geometry, since it has a cube in it. For the solution we need conic sections.’ —Omar Khayyam (who not only not only put his toes into non-Euclidean waters, he is also given credit by some art historians for the design of the North Dome chamber of Esfahan’s Friday Mosque, built in 1088.)
