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Islamic Design and Its Relation to Mathematics

  • Brian WichmannEmail author
  • David Wade
Living reference work entry

Abstract

Complex geometrical designs are a familiar feature of Islamic art. Here we consider the historical context of this genre, tracing it back to the influence of the Platonism and Hellenistic Neo-Platonism that Islam encountered in its early conquest of Byzantine territories (in particular the enormous contribution of Euclid).

In addition, the modern analysis is presented showing the relationship in mathematical terms. Such an analysis naturally leads to the presentation of the patterns using computer graphics.

Keywords

Islamic design Geometry Historic influences Modern graphics 

References

  1. Al-Khalili J (2010) Pathfinders. Allen Lane, New YorkGoogle Scholar
  2. Allen T (2004) Islamic art and the argument from academic geometry. Solipsist Press, Weidenfield & NicholsonGoogle Scholar
  3. Al-Naqsh MM (1983) Design and execution of drawing in Iranian tilework, Islamic period. Reza Abbasi Museum, (In Persian)Google Scholar
  4. Blair SS (2006) Islamic calligraphy. Edinburgh University Press, EdinburghGoogle Scholar
  5. Bloom JM (2001) Paper before print: the history and impact of paper in the Islamic world. Yale University Press, New HavenGoogle Scholar
  6. Bloom JM (2007) Arts of the city victorious. Yale, New HavenGoogle Scholar
  7. Bonner J (2016) Islamic geometric patterns. Springer. ISBN:9781441902160zbMATHGoogle Scholar
  8. Bourgoin J (1873) Les arts arabes. Morel, ParisGoogle Scholar
  9. Bourgoin J (1879) Les Eléments de l’art arabe: le trait des entrelacs, Paris (Patterns available as a Dover reprint)Google Scholar
  10. Broug E (2008) Islamic geometric patterns. Thames & Hudson, LondonGoogle Scholar
  11. Broug E (2013) Islamic geometric design. Thames and Hudson, LondonGoogle Scholar
  12. Castéra J-M (1999) Arabesques: decorative art in Morocco. ACR Edition, ParisGoogle Scholar
  13. Chorbachi WK (1989) In the tower of babel: beyond symmetry in Islamic design. Comput Math Appl 17(4–6):751–789MathSciNetCrossRefGoogle Scholar
  14. De Boer TJ (1903) The history of philosophy in Islam. Luzac, LondonGoogle Scholar
  15. Du Sautoy M (2008) Finding moonshine—a mathematician’s journey through symmetry. Fourth Estate, London. ISBN:978-0-00-721467-2zbMATHGoogle Scholar
  16. Freely J (2009) Aladdin’s lamp: how Greek science came to Europe through the Islamic world. Alfred A. Knoopf, New YorkGoogle Scholar
  17. Grabar O (1973) The formation of Islamic art. Yale University Press, New HavenGoogle Scholar
  18. Grünbaum B (2006) What groups are present in the Alhambra? Not Am Math Soc 53:670–673. http://www.ams.org/notices/200606/comm-grunbaum.pdf MathSciNetzbMATHGoogle Scholar
  19. Grünbaum B, Shephard GC (1987) Tilings and patterns. W. H. Freeman & Co., New YorkzbMATHGoogle Scholar
  20. Jagy W (2000) What Islamic tiling patterns are constructible? http://mathoverflow.net/questions/35526
  21. Jaworski J (2006) A mathematician’s guide to the alhambra. Available on the Internet via http://www.grout.demon.co.uk/Travel/travel.htm
  22. Jones O (1856) The grammar of ornament. Dover. (reprint) Original version available on the InternetGoogle Scholar
  23. Jones O, Goury J (1837) Plans, elevations, sections, and details of the Alhambra…. O. Jones, LondonGoogle Scholar
  24. Kennedy H (2005) When Baghdad ruled the Muslim world. Da Capo Press, CambridgeGoogle Scholar
  25. Khaldun I (1967) In: Dawood NA (ed) The Muqaddimah: an introduction to history (trans: Franz Rosenthal). Princeton University Press, Princeton, Routledge and Kegan PaulGoogle Scholar
  26. Kühnel E (1949) Arabesques. Verlag für SammlerGoogle Scholar
  27. Lee AJ (1987) Islamic star patterns. Muqarnas 4:182–197CrossRefGoogle Scholar
  28. Lee T, Soliman A (2014) The geometric rosette: analysis of an Islamic decorative motif. http://www.tilingsearch.org
  29. Montesinos JM (1985) Classical tessellations and three-manifolds. Springer. ISBN:3-540-15291-1zbMATHGoogle Scholar
  30. Montgomery Watt W (1972) The influence of Islam on medieval Europe. Edinburgh University Press, EdinburghGoogle Scholar
  31. Morewedge P (ed) (1992) Neoplatonism and Islamic thought. University of New York, AlbanyGoogle Scholar
  32. Müller E (1944) Gruppentheoretische und Strukturanalytische Untersuchungen der Maurischen Ornamente aus der Alhambra in Granada. PhD thesis, Zürich University. Baublatt, RüschlikonGoogle Scholar
  33. Necipoğlu G (1995) The Topkapı scroll: geometry and ornament in Islamic architecture. The Getty Center for the History of Art and the Humanities, Santa MonicaGoogle Scholar
  34. Özdural A (2000) Mathematics and arts: connections between theory and practice in the medieval Islamic world. Hist Math 27:171–201MathSciNetCrossRefGoogle Scholar
  35. Paccard A (1980) Traditional Islamic craft in Moroccan architecture. Saint-Jorioz, AtelierGoogle Scholar
  36. Routledge, Kegan P (1975) The classical heritage in Islam. University of California Press, BerkeleyGoogle Scholar
  37. Saliba G (2011) Islamic science and the making of the European renaissance. MIT Press, CambridgeGoogle Scholar
  38. Tiling search web site (2019) www.tilingsearch.org. Graphics refer to a specific web site URL, e.g., data162/P077 gives the www.tilingsearch.org/HTML/data162/P077.html
  39. Wade D (2018) Patterns in Islamic art. The web site: www.patterninislamicart.com. Photos reference in the format EGY 0512
  40. Wichmann BA (2001) The world of patterns. World Scientific. ISBN:981024619Google Scholar
  41. Wichmann B, Rigby J (2009) Yemeni squares. MIT Press, Leonardo 42(2):156–162CrossRefGoogle Scholar
  42. Wichmann B, Wade D (2017) Islamic design: a mathematical approach. Birkhäuser, ChamCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Independent ScholarWokingUK
  2. 2.Independent ScholarLlanidloesUK

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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