Saturday, January 12, 2008

293)Symmetry in nature; Symmetry as a product of the human mind: Part deux.

This post is now part of the following collection of posts:
454)A Collection of Posts on Symmetry in Nature, as a Product of the Human Mind, Geometry and Harmonious Mathematical Reasoning; Quotes of Aga Khan IV

Medieval Mosque Shows Amazing Math Discovery

The never-repeating geometry of quasi crystals, revealed 500 years early
by John Bohannon

The mosques of the medieval Islamic world are artistic wonders and perhaps mathematical wonders as well. A study of patterns in 12th- to 17th-century mosaics suggests that Muslim scholars made a geometric breakthrough 500 years before mathematicians in the West.

Peter J. Lu, a physics graduate student at Harvard University, noticed a striking similarity between certain medieval mosque mosaics and a geometric pattern known as a quasi crystal—an infinite tiling pattern that doesn’t regularly repeat itself and has symmetries not found in normal crystals (see video below). Lu teamed up with physicist Paul Steinhardt of Princeton University to test the similarity: If the patterns repeated when extended infinitely, they couldn’t be true quasi crystals.

Most of the patterns examined failed the test, but one passed: a pattern found in the Darb-i Imam shrine (seen in the first video above), built in 1453 in Isfahan, Iran. Not only does it never repeat when infinitely extended, its pattern maps onto Penrose tiles—components for making quasi crystals discovered by Oxford University mathematician Roger Penrose in the 1970s—in a way that is consistent with the quasi crystal pattern.

Among the 3,700 tiles Lu and Steinhardt mapped, there are only 11 tiny flaws, tiles placed in the wrong orientation. Lu argues that these are accidents possibly introduced during centuries of repair. “Art historians always suspected there must be something more to these patterns,” says Tom Lentz, director of Harvard University Art Museums, but they were never examined with “this kind of scientific rigor.”

Easy Nash aka easynash

The Qur'an itself repeatedly recommends Muslims to become better educated in order better to understand God's creation: Aga Khan IV(2007)
The Quran tells us that signs of Allah's Sovereignty are found in the contemplation of His Creation: Aga Khan IV(2007)
This notion of the capacity of the human intellect to understand and to admire the creation of Allah will bring you happiness in your everyday lives: Aga Khan IV(2007)
Islam, eminently logical, placing the greatest emphasis on knowledge, purports to understand God's creation: Aga Khan IV(2006)