Nexus Network Journal

, Volume 17, Issue 1, pp 157–181 | Cite as

Nonagons in the Hagia Sophia and the Selimiye Mosque



One of the classical topics in geometry is the ruler and compass construction of good approximations of the regular nonagon. We propose a method to choose a desired error of approximation, based on new linear third-order recurrence relations. It is related to patterns shown on the balustrade of minbar of Selimiye Mosque in Edirne (Turkey, 1569–1575), where apparently regular nonagons are placed over a net of regular hexagons. This kind of ornament also occurs in Hagia Sophia in the minbar, in freezes stucco carvings and in window grilles. In Medieval Islamic art and architecture the use of the nonagon is not frequent, but it is remarkable that this particular grid of interlocked nonagons and hexagons appears in the decorations of the works of Ottoman architect Mimar Sinan. The pattern is present in his masterpiece, the Selimiye Mosque, in the Hagia Sophia and in other works in the Istanbul city. Looking at practical ways for the construction of the pattern, we provide simple procedures to obtain angles close to 40° that could have been useful for a craftsman to realize the nonagonal geometric designs. In particular, almost regular nonagons are constructed using some elementary shapes that are related with semi-regular tessellations. We compare the patterns obtained through theoretical considerations to those displayed in the examples given above. Several hypotheses are proposed for the practical construction of the interlocked hexagonal patterns for nonagons.


Ruler and compass construction Nonagon Selimiye Mosque Hagia Sophia Minbar Mimar Sinan 


  1. Al-Biruni. 1954–1956 A.D./1373-1375 A.H, Al-Qanunu’l-Mas’udi (Canon Masudicus). Hyderabad: Osmania Oriental Publication Bureau. 3 vols.Google Scholar
  2. Grünbaum, Branko, Shepard, Geoffrey C. 1987. Tilings and Patterns. New York: W.H. FreemanGoogle Scholar
  3. Hogendijk, Jan P. 1979. On the trisection of an angle and the construction of a regular nonagon by means of conic sections in medieval Islamic geometry, unpublished ms., Preprint 113, March 1979, University of Utrecht, Department of Mathematics. Retrieved from, 19 Dec. 2014.
  4. Kappraff, Jay, Jablan, Slavik, Adamson, Gary W. and Sazdanovic, Radmila. 2004. Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices. Forma 19: 367–387.Google Scholar
  5. Özdural, A. 1996. On Interlocking Similar or Corresponding Figures and Ornamental Patterns of Cubic Equations.Muqarnas13: 191–211.Google Scholar
  6. Özdural, A. 2002. The Use of Cubic Equations in Islamic Art and Architecture. pp. 165–179 in Nexus IV: Architecture and Mathematics, Kim Williams and Jose Francisco Rodrigues, eds. Fucecchio (Florence): Kim Williams Books. Rpt. in Architecture and Mathematics from Antiquity to the Future, vol. I, Kim Williams and Michael J. Ostwald, eds., Cham, Springer, 2014, pp. 467–482.Google Scholar
  7. Steinbach, Peter. 1997. Golden Fields: A Case for the Heptagon. Mathematics Magazine 70: 22–31.Google Scholar

Copyright information

© Kim Williams Books, Turin 2015

Authors and Affiliations

  1. 1.Departamento de MatemáticasI.E.S. Bachiller SabucoAlbaceteSpain
  2. 2.LUCA School of Arts KU LeuvenBrusselsBelgium

Personalised recommendations