<p>The mosques of the medieval Islamic world are artistic wonders and perhaps mathematical wonders as well. A <a href="http://www.sciencemag.org/cgi/content/short/315/5815/1106" title="">study</a> of patterns in 12th- to 17th-century mosaics suggests that Muslim scholars made a geometric breakthrough 500 years before mathematicians in the West.</p><div class="vert-display-toggle collapsible relative flex flex-col items-center "><div class="vert-unit mt-4 mb-3 top-20"><div ad-type="mobile-desktop" class="ad-wrapper vert min-h-boombox flex items-start justify-center" data-ad-mapping="inline" data-ad-slot="Discover/inline-ad" id="div-inline-ad-0"></div></div><span aria-label="Advertisement" class="text-ad mt-1 text-[11px] uppercase">Advertisement</span></div><p>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.</p><span class="fr-video"><div id="content-id-11986-body-iframe-idx-0"></div></span><span class="fr-video"><div id="content-id-11986-body-iframe-idx-1"></div></span><span class="fr-video"><div id="content-id-11986-body-iframe-idx-2"></div></span><span class="fr-video"><div id="content-id-11986-body-iframe-idx-3"></div></span><p>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 <a href="http://en.wikipedia.org/wiki/Penrose_tiling" title="">Penrose tiles</a>—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.</p><div data-embedid="4b651d8f-ea11-445f-9ea7-e776ca36eef3" id="insticator-embed-temp"></div><p>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.”</p><p><strong>Go to the next story: </strong><a href="https://discover.ac.cn/~/link.aspx?_id=28C9B0D151304076AE95F88DE60E139F&amp;_z=z" title="">60. Diamonds From Outer Space</a></p>

January 2008

The January 2008 issue of Discover Magazine

100 Top Science Stories of 2017

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

The Sciences

59. Medieval Mosque Shows Amazing Math Discovery

Article

News

John Bohannon

Science

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.” Go to the next story: 60. Diamonds From Outer Space

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