Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture

Images: (click to enlarge)
Colloquium Lecture: Harvard University Physics Department (Dec 07)
Interview: NPR's All Things Considered (Feb 2007)
Interview: BBC's The World Today (Feb 2007)
Interview: Deutschlandfunk's Forschung Aktuell [Germany] (Feb 07)
Interview: WHRB Harvard Radio (Feb 2007)
Gunbadi Kabud
Darbi Imam Tiles
Intimad AlDaula
Topkapi Scroll

The conventional view holds that girih (geometric star-and-polygon) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (girih tiles) decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.

Press: 
“The Tiles of Infinity,” Saudi Aramco World  (Sep 2009)
“Top 100 Science Stories of 2007: 59. Medieval Mosque Shows Amazing Math Discovery,” Discover  (Jan 2008)
“Geometrische Schönheiten,” Berliner Zeitung [Germany]  (Feb 2007)
“Islamic artists were 500 years ahead of Western scientists,” The Independent [UK]  (Feb 2007)
“Moderne Mathematik in islamischen Ornamenten,” Spektrum der Wissenschaft [Germany]  (Sep 2007)
“Moschee-Baumeister waren westlichen Mathematikern 500 Jahre voraus,” Der Spiegel [Germany]  (Feb 2007)
“Quasikristalline islamische Muster,” Spektrum der Wissenschaft [Germany]  (May 2007)
“Puzzle der Unendlichkeit,” Die Zeit [Germany]  (Feb 2007)
“New light on ancient patterns ; Sophisticated Islamic geometric designs in Iran predate Western discovery by 500 years,” Chicago Tribune  (Feb 2007)
“Islamische Kunst: Fliesen verblüffen Mathematiker,” Focus [Germany]  (Feb 2007)
“Modern mathematicians are 500 years behind,” The Globe and Mail [Canada]  (Feb 2007)
“Matematiker avslöjade koden till islamska mönster,” Dagens Nyheter [Sweden]  (Mar 2007)
“Mathematik und Kunst beim Plattenlegen,” Neue Zürcher Zeitung [Switzerland]  (Mar 2007)
“Wzory zagubione na pół tysiąca lat,” Gazeta Wyborcza [Poland]  (Feb 2007)
“Islamische Ornamente,” Neue Zürcher Zeitung [Switzerland]  (Mar 2007)
“Il segreto dell’architettura islamica medioevale `Usa formule matematiche del XX secolo',” La Repubblica [Italy]  (Feb 2007)
“MISTERI `Ho trovato i numeri dell'infinito nei grandi mosaici dell'Islam',” La Stampa [Italy]  (Apr 2007)
“Matemática muito 'à frente' explica mosaicos islâmicos,” Diario de Noticias [Portugal]  (Feb 2007)
“L’art des mosquées devance les maths,” El Watan [Algeria]  (Jun 2007)
“Medieval Islamic artists made amazing maths breakthrough,” Gulf News [United Arab Emirates]  (Feb 2007)
“Medieval Muslims made stunning maths breakthrough,” Gulf Times [Qatar]  (Feb 2007)
“Medieval Muslims made stunning math breakthrough,” Today's Zaman [Turkey]  (Feb 2007)
“Medieval Muslims made stunning maths breakthrough,” The Times of India  (Feb 2007)
“Medieval math feat,” The Telegraph [Calcutta, India]  (Feb 2007)
“Patterns of Islamic Genius Crystal Clear Centuries Ago,” Sydney Morning Herald [Australia]  (Feb 2007)
“In Medieval Architecture, Signs of Advanced Math,” The New York Times  (Feb 2007)
“Designs from Islamic artists streets ahead of West,” New Zealand Herald  (Feb 2007)
“Higher Math From Medieval Islam,” Newsweek  (Mar 2007)
“이슬람 문양 규칙성 찾았다… “4, 5개 단위로 묶으면 패턴”,” dongA [South Korea]  (Feb 2007)
“Science imitates art?,” The Boston Globe  (Feb 2007)
“Los mosaicos árabes, geometría de avanzada,” La Nacion [Argentina]  (Feb 2007)
“Muslim Tile Patterns Show Math Prowess,” The Washington Post  (Feb 2007)
“The art of repetition,” National Post [Canada]  (Feb 2007)
“Amazing maths of the mosaic makers,” The Times [UK]  (Feb 2007)
“Islamisk kunst forud for sin tid,” Politiken [Denmark]  (Feb 2007)
“Islamic tilers may have led scientific field,” The Daily Telegraph [UK]  (Feb 2007)
“Medieval Islamic tiling reveals mathematical savvy,” New Scientist  (Feb 2007)
“Islamic tiles reveal sophisticated maths,” Nature  (Feb 2007)
“Ancient Islamic Penrose Tiles ,” Science News  (Feb 2007)
“Islamic Artisans Constructed Exotic Nonrepeating Pattern 500 Years Before Mathematicians,” Scientific American  (Feb 2007)
“Angewandte Mathematik: Das Geheimnis der Girih,” Spektrum der Wissenschaft [Germany]  (Feb 2007)
“Das Geheimnis der islamischen Kachelmosaike,” Bild der Wissenschaft [Germany]  (Feb 2007)
“Cinq siècles d'avance !,” Pour la Science [France]  (May 2007)
“Medieval Islamic architecture presages 20th century mathematics,” Harvard Gazette  (Mar 2007)

Peter J. Lu  |  Harvard University  |  Cambridge, MA 02138 USA |  plu_at_fas.harvard.edu