Medieval Muslims made stunning math breakthrough

By Will Dunham 2 hours, 25 minutes ago

Medieval Islamic artisans developed a pattern-making process for designing ornate tiled surfaces that allowed them to produce sophisticated patterns not seen in the West until centuries later, a new study suggests. Many walls of medieval Islamic buildings have ornate geometric star-and-polygon, or girih, patterns, often overlaid with a zig-zagging network of lines. This undated picture shows an archway from the Darb-i Imam shrine, Isfahan, Iran ( built in 1453 ) with two overlapping girih patterns. REUTERS/handout/K. Dudley and M. Elliff.

WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.

By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasicrystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.

Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.

"Oh, it's absolutely stunning," Lu said in an interview. "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years."

Lu and Steinhardt in particular cite designs on the Darb-i Imam shrine in Isfahan,
Iran, built in 1453.

Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns.

The walls of many medieval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs.

"You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex" over time, Lu added.

ISLAMIC ACHIEVEMENTS

While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas.

Lu said the new revelations suggest Islamic culture was even more advanced than previously thought.

While traveling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasicrystalline Islamic tilings.

The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide.

Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasicrystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran.

Joshua Socolar, a Duke university physicist, said it is unclear whether the medieval Islamic artisans fully understood the mathematical properties of the patterns they were making.

"It leads you to wonder whether they kind of got lucky," Socolar said in an interview. "But the fact remains that the patterns are tantalizingly close to having the structure that Penrose discovered in the mid-70s."

"And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show," Socolar said.

http://news.yahoo.com/s/nm/20070223/sc_nm/architecture_patterns_dc

Here's the wikipedia entry on Penrose Tilings:

http://en.wikipedia.org/wiki/Penrose_tiling

And here's a more detailed description of the patterns found in Islamic architecture:

http://blog.sciencenews.org/mathtrek/2007/02/ancient_is...penrose_tiles_1.html

Here's the original Science article, with supporting materials from the author's webpage:

Peter J. Lu and Paul J. Steinhardt "Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture," Science 315, 1106 (2007)

Original Article: http://www.physics.harvard.edu/~plu/publications/Science_315_1106_2007.pdf

Supporting Online Material: http://www.physics.harvard.edu/~plu/publications/Science_315_1106_2007_SOM.pdf

Peace...

Great article..Thanks