Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture

Quasicrystalline Tiling

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.

 

Related Links

General-Audience Radio Broadcasts:
  • "Medieval Mosques Illuminated by Math," National Public Radio: All Things Considered [ link ]
  • "Advanced geometry of Islamic art," BBC World Service: The World Today [ mp3 (5 MB) ] [ news.bbc.co.uk ]
Mainstream Newspapers and Magazines: (** indicates front-page print-edition coverage)
  • **"Advanced Math in Medieval Architecture," The New York Times [ link ]
  • **"Amazing maths of the mosaic makers," The Times (London) [ link ]
  • **"New light on ancient patterns," The Chicago Tribune [ link ]
  • **"Science Imitates Art?" The Boston Globe [ link ]
  • **"Modern math in medieval tiles," International Herald Tribune [ link ]
  • **"Medieval Islamic artists made amazing maths breakthrough," Gulf News (United Arab Emirates) [ link ]
  • **"Medieval Muslims made stunning math breakthrough," Today's Zaman (Turkey) [ link ]
  • **"Early Muslims made amazing math inventions," Brunei Times (Brunei) [ link ]
  • "Islam Got It First," Newsweek (Intl. Ed.) [ link ]
  • "Islamic tilers may have led scientific field," The Daily Telegraph (London) [ link ]
  • "Medieval Muslims made stunning maths breakthrough," The Times of India [ link ]
  • "Medieval math feat," The Telegraph of India [ link ]
  • "Patterns of Islamic genius crystal clear centuries ago," Sydney Morning Herald (Australia) [ link ]
  • "Designs from Islamic artists streets ahead of West," New Zealand Herald (New Zealand) [ link ]
  • "Islamic artists were 500 years ahead of Western scientists," The Independent (London) [ link ]
  • "Modern mathematicians are 500 years behind," The Globe and Mail (Canada) [ link ]
  • "The art of repetition," National Post (Canada) [ link ]
  • "Muslim Tile Patterns Show Math Prowess," The Washington Post [ link ]
  • "Medieval Islamic Architecture Predates Western Mastery," The Iran Daily (Iran) [ link ]
  • "Medieval Muslims made stunning breakthrough," Bahrain Tribune (Bahrain) [ link ]
  • "Study may change view of mathematical origins," Newsday (New York) [ link ]
  • "Medieval Muslims made stunning maths breakthrough," Gulf Times (Qatar) [ link ]
  • "Medieval Islamic architecture presages 20th century mathematics," Harvard University Gazette [ link ]
  • "Medieval Muslims made stunning math breakthrough," Reuters [ link ]
  • "Geometry meets artistry in medieval tilework," AP/CNN.com [ link ]

    • Non-English

  • **"Matematiker avsljade koden till islamska mnster," Dagens Nyheter (Sweden) [ link ]
  • "Il segreto dell'architettura islamica medioevale 'Usa formule matematiche del XX secolo'," La Repubblica (Italy) [ link ]
  • "Puzzle der Unendlichkeit," Die Zeit (Germany) [ link ]
  • "Moschee-Baumeister waren westlichen Mathematikern 500 Jahre voraus," Der Spiegel (Germany) [ link ]
  • "El arte de las matemticas," ABC (Spain) [ link ]
  • "Matemática muito 'à frente' explica mosaicos islâmicos," Diario de Noticias (Portugal) [ link ]
  • "Islamisk kunst forud for sin tid," Politiken (Denmark) [ link ]
  • "Los mosaicos rabes, geometra de avanzada," La Nacion (Argentina) [ link ]
  • Donga (Korea) [ link ]
  • "Islamische Kunst: Fliesen verblüffen Mathematiker," Focus (Germany) [ link ]
  • "Geometrische Schnheiten," Berliner Zeitung (Germany) [ link ]
  • "Des mosaques arabo-islamiques mdivales tmoignent d'une gomtrie avance", AFP/fr.yahoo.com (France) [ link ]
Science-Oriented Publications
  • "Islamic tiles reveal sophisticated maths", Nature.com [ link ]
  • "Medieval Islamic tiling reveals mathematical savvy", NewScientist.com [ link ]
  • "Ancient Islamic Penrose Tiles", Sciencenews.org [ link ]
  • "Islamic Artisans Constructed Exotic Nonrepeating Pattern 500 Years Before Mathematicians", Scientific American online [ link ]
  • "Islamic 'quasicrystals' predate Penrose tiles", PhysicsWeb.org [ link ]
  • "Medieval Islamic Mosaics Used Modern Math", LiveScience.com [ link ]
  • "Medieval Islamic quasi-periodic tilings," Math in the Media from the AMS [ link ]

    • Non-English

  • "Quasikristalle im Ornament", Deutschlandfunk: Forschung Aktuell (Germany) [ link ]
  • "Das Geheimnis der Girih", SpektrumDirect (Germany) [ link ]
  • "Das Geheimnis der islamischen Kachelmosaike", Wissenschaft.de (Germany) [ link ]
  • "Vijf tegels voor Allah", noorderlicht.vpro.nl (The Netherlands) [ link ]
Additional Online Links
  • "The Universal Language," Encyclopaedia Britannica Blog [ link ]
  • "U.S. Academics Say Medieval Islamic Designers Knew Their Math," Radio Free Europe / Radio Liberty [ link ]

    • Non-English

  • "مسلمان نقاش پانچ سو سال قبل بیسویں صدی کی ریاضی کے اصولوں سے واقف تھے", Voice of America/Urdu (USA/Pakistan) [ link ]
  • "Sanat ve matematik", BBCTurkish.com (UK/Turkey) [ link ]
  • "Исломий санъат илғор ҳандасага эга бўлган", BBCUzbek.com (UK/Uzbekistan) [ link ]
  • "اسلامی تعمیر میں جدید جیومیٹری", BBCUrdu.com (UK/Pakistan) [ link ]
  • "Geometri dalam seni Islam", BBCIndonesian.com (UK/Indonesia) [ link ]
  • "Hình học trong nghệ thuật Hồi giáo", BBCVietnamese.com (UK/Indonesia) [ link ]
  • "Sofisticada geometra en el arte islmico", BBCMundo.com (UK/Spain) [ link ]
  • "Arte islmica medieval usava matemtica moderna, diz estudo", BBCBrazil.com (UK/Brasil) [ link ]
  • "Arte islâmica desvenda segredos da matemática", BBCParaAfrica.com (UK/Africa) [ link ]