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The Decagonal Tomb Tower at Maragha and Its Architectural Context: Lines of Mathematical Thought

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Persian Architecture and Mathematics

Part of the book series: Nexus Network Journal ((NNJ))

Abstract

Of several brick tomb towers constructed at Maragha in western Iran before the Mongol conquests, one in particular, Gonbad-e Qabud (593 H. / 1196–97 C.E.), has generated significant recent attention for its unique patterns with pentagons and decagons. Gonbad-e Qabud is also unusual in having a decagonal plan. While both plan and decoration distinguish it from earlier and later towers at Maragha and elsewhere on the Iranian plateau, the ornamental patterns follow a long line of experimentation with geometric expressions that grace many pre-Mongol buildings in Iran. This article examines in particular the overlapping polygons and radial symmetries of the tympanum of the cubic Gonbad-e Sork (542 H. / 1148 C.E.) at Maragha, and the pentagons and squares of the tympanum of the later octagonal tomb tower (486 H. / 1093 C.E.) nearby at Kharraqan. Drawing from archival sources (plans, elevations, photographs), analysis of plane patterns, and comparative architectural data, this article reevaluates the cultural significance of Gonbad-e Qabud, seeking to situate it within the histories of mathematics, architecture, and the arts.

Carol Bier is a Visiting Scholar (2010–12) with the Center for Islamic Studies at the Graduate Theological Union in Berkeley CA and Research Associate at The Textile Museum in Washington DC (2001–12), where she served as Curator for Eastern Hemisphere Collections (1984–2001). Her current research focuses on the historical development of Islamic patterns as intersections of geometry, art, religion, and philosophy.

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References

  • ALI, A.Y. 1978. The Holy Qur’an: Text, Translation and Commentary. Washington D.C.: The Islamic Center.

    Google Scholar 

  • BERGGREN, J. L. 2007. Mathematics in Medieval Islam. Pp. 515–675 in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, V.J. Katz, ed. Princeton: Princeton University Press.

    Google Scholar 

  • BIER, C. 2002. Geometry and the Interpretation of Meaning: Two Monuments in Iran. Pp. 67–78 in Bridges: Mathematical Connections in Art, Music, and Science, R. Sarhangi, ed. Winfield KS.

    Google Scholar 

  • -. 2004. Pattern Power: Textiles and the Transmission of Mathematical Knowledge. Pp. 144–153 in Appropriation, Acculturation, Transformation: Proceedings of the 9th Biennial Symposium of the Textile Society of America, C. Bier, ed. Textile Society of America.

    Google Scholar 

  • -. 2007. Patterns in Time and Space: Technologies of Transfer and the Cultural Transmission of Mathematical Knowledge across the Indian Ocean. Ars Orientalis 34: 174–196.

    Google Scholar 

  • -. 2008. Art and Mithal: Reading Geometry as Visual Commentary. Iranian Studies 41, 4: 491–509.

    Article  Google Scholar 

  • -. 2009. Number, Shape, and the Nature of Space: Thinking through Islamic Art. Pp. 827–851 in Oxford Handbook for the History of Mathematics. E. Robson and J. Stedall, eds. Oxford: Oxford University Press.

    Google Scholar 

  • -. 2011a. Taking Sides, but Who’s Counting? The Decagonal Tomb Tower at Maragha. Pp. 497–500 in Bridges Conference (Mathematical Connections in Art, Music, Science, R. Sarhangi, et al., eds. Phoenix: Tessellations Publishing.

    Google Scholar 

  • -. 2011b. Qur’an, Amthal, and Geometry on the Iranian Plateau in the 11th and 12th Centuries. Presented at “Workshop: Cultural Responses to the Qur’an”, 18 November 2011, American Academy of Religion Annual Meeting (AAR), San Francisco. Forthcoming.

    Google Scholar 

  • BLAIR, S. 1992. The Monumental Inscriptions from Early Islamic Iran and Transoxiana. New York: E. J. Brill.

    Google Scholar 

  • BLAIR, S. 2004. IL-KHANIDS ii. ARCHITECTURE. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/il-khanids-ii-architecture. Last accessed 6 April 2012.

    Google Scholar 

  • BONNER, J. 2003. Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century Islamic Geometric Ornament. Pp. 1–12 in Meeting Alhambra: ISAMA-Bridges Conference Proceedings. J. Barrallo, et al., eds. Granada: University of Granada.

    Google Scholar 

  • CHORBACHI, W. K. 1989. In the Tower of Babel: Beyond Symmetry in Islamic Design. Computers and Mathematics with Applications 17: 751–789 (rpt. in Symmetry 2: Unifying Human Understanding, I. Hargittai, ed. New York: Pergamon, 1989, pp. 751–789).

    Article  MathSciNet  Google Scholar 

  • CHORBACHI W.K. and A. LOEB. 1992. An Islamic Pentagonal Seal (from Scientific Manuscripts of the Geometry of Design). Pp. 283–305 in Fivefold Symmetry, I. Hargittai, ed. Singapore: World Scientific.

    Chapter  Google Scholar 

  • CROMWELL, P. R. 2009, The Search for Quasi-Periodicity in Islamic 5-Fold Ornament. Mathematical Intelligencer 31, 1: 36–56.

    Article  MATH  MathSciNet  Google Scholar 

  • -. 2010. Hybrid 1-point and 2-point Constructions for Some Islamic Geometric Designs. Journal of Mathematics and the Arts 4, 1: 21–28.

    Article  MATH  Google Scholar 

  • DANESHVARI, A. 1982. Complementary Notes on the Tomb Towers of Medieval Iran. 1: The Gunbad-i Kabud at Maraghe 593/1197. Pp. 287–295 in Art et Sociéte dans le Monde Iranien, C. Adle, ed. Paris: Editions Recherche sur les civilisations.

    Google Scholar 

  • -. 1986. Medieval Tomb Towers of Iran. Malibu: Undena Press.

    Google Scholar 

  • DE BLOIS, F. 2002. HAFT PEYKAR. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/haft-peykar. Last accessed 6 April 2012.

    Google Scholar 

  • FLEURENT, G. M. 1992. Pentagon and Decagon Designs in Islamic Art. Pp.263–281 in Fivefold Symmetry, I. Hargittai, ed. Singapore: World Scientific.

    Chapter  Google Scholar 

  • GODARD, A. 1934. Les Monuments de Marāgha. Publications of the Société des études iraniennes, no. 7. Paris: E. Leroux.

    Google Scholar 

  • -. 1936. Notes Complementaires sur les Tombeaux de Maragha. Athar-e-Iran 1: 125–60.

    Google Scholar 

  • GRABAR, O. 1990. The Great Mosque of Isfahan. New York: New York University Press.

    Google Scholar 

  • -. 1993. The Mediation of Ornament. Princeton: Princeton University Press.

    Google Scholar 

  • GRÜNBAUM, B. and G. C. SHEPHARD. 1989. Tilings and Patterns: An Introduction. New York: W.H. Freeman and Company.

    MATH  Google Scholar 

  • HILLENBRAND, R. 1982, The Flanged Tomb Tower at Bastam. Pp. 237–261 in Art et Sociéte dans le Monde Iranien, C. Adle, ed. Paris: Editions Recherche sur les civilisations.

    Google Scholar 

  • -. 1994. Islamic Architecture: Form, Function, Meaning. New York: Columbia University Press.

    Google Scholar 

  • HOURCADE, B. 1984. ALAMŪT. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/alamut-valley-alborz-northeast-of-qazvin-. Last accessed 6 April 2012.

    Google Scholar 

  • JACKSON, P. 2005. Mongols and the West. New York: Longman.

    Google Scholar 

  • KAPLAN, C. S. 2005. Islamic Star Patterns from Polygons in Contact. GI’ 05: Proceedings of the 2005 Conference on Graphics Interface. http://www.cgl.uwaterloo.ca/~csk/papers/ kaplan_gi2005.pdf. Last accessed 6 April 2012.

    Google Scholar 

  • KHEIRANDISH, E. 2008. Science and Mithal: Demonstrations in Arabic and Persian Scientific Traditions. Iranian Studies 41, 4: 465–89.

    Article  MathSciNet  Google Scholar 

  • KLEISS, W. 2002. AZERBAIJAN xii. MONUMENTS. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/azerbaijan-monuments. Last accessed 6 April 2012.

    Google Scholar 

  • KOMAROFF, L. and S. CARBONI, eds. 2002. The Legacy of Genghis Khan: Courtly Art and Culture in Western Asia, 1256–1353. New York: The Metropolitan Museum of Art.

    Google Scholar 

  • KORN, L. 2010. SALJUQS vi. ART AND ARCHITECTURE. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/saljuqs-vi. Last accessed 6 April 2012.

    Google Scholar 

  • LEE, A. J. 1987. Islamic Star Patterns. Muqarnas 4: 182–197.

    Article  Google Scholar 

  • LU, P. J. and P. J. STEINHARDT. 2007a. Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture,” Science 315 (Feb. 22): 1106–1110. (Supp. Online Material, figs. S1–S8, www.sciencemag.org/cgi/content/full/315/5815/[page]DC1)

    Article  MATH  MathSciNet  Google Scholar 

  • -. 2007b. Response to ‘Comment on “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. Science 318 (November 30): 1383.

    Article  MathSciNet  Google Scholar 

  • LUTHER, K. A. 1987. ATĀBAKĀN-E MARĀGA. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/atabakan-e-maraga-also-called-ahmadilis-afamily-of-local-rulers-of-maraga-who-ruled-from-the-early-6th-12th-cent. Last accessed 6 April 2012.

    Google Scholar 

  • MAKOVICKY, E. 1992. 800-Year-Old Pentagonal Tiling from Maragha, Iran, and The New Varieties of Aperiodic Tiling It Inspired. Pp. 67–86 in Fivefold Symmetry, I. Hargittai, ed. Singapore: World Scientific.

    Chapter  Google Scholar 

  • -. 2007. Comment on ‘Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. Science 318 (November 30): 1383a.

    Article  Google Scholar 

  • -. 2008. Another Look at the Blue Tomb of Maragha, A Site of the First Quasicrystalline Islamic Pattern. Symmetry: Culture and Science 19, 2–3: 127–151.

    Google Scholar 

  • MILWRIGHT, M. 2001. GEREH-SAZI ii. ARCHITECTURE. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/gereh-sazi. Last accessed 6 April 2012.

    Google Scholar 

  • -. 2002. GONBAD-E SORK. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/gonbad-e-sork. Last accessed 6 April 2012.

    Google Scholar 

  • MINORSKY, V.. 1960. Ahmadīlīs. Encyclopaedia of Islam, 2nd ed., P. Beam, et al., eds., vol. 1, pp. 300–301. Leiden: E. J. Brill

    Google Scholar 

  • -. 2011. Marāgha. Encyclopedia of Islam, 2nd ed. P. Beam, et al., eds., vol. ?, pp. ??-??. Leiden: Brill.

    Google Scholar 

  • NECIPOĞLU, G. 1995 The Topkapi Scroll: Geometry and Ornament in Islamic Architecture. Santa Monica: Getty Center for the History of Art and the Humanities.

    Google Scholar 

  • O’KANE, B. 2009. The Appearance of Persian on Islamic Art. New York: Persian Heritage Foundation.

    Google Scholar 

  • ÖZDURAL, A. 1995. “Omar Khayyam, Mathematicians, and Conversazioni with Artisans,” Journal of the Society of Architectural Historians 54, 1 (March 1995): 54–71.

    Article  Google Scholar 

  • -. 1996. On Interlocking Similar or Corresponding Figures and Ornamental Patterns of Cubic Equations. Muqarnas 13: 191–211.

    Article  MathSciNet  Google Scholar 

  • -. 1998, A Mathematical Sonata for Architecture: Omar Khayyam and the Friday Mosque of Isfahan. Technology and Culture 39, 4: 699–715.

    Google Scholar 

  • -. 2000. Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World. Historia Mathematica 27, 2: 171–201.

    Article  MATH  MathSciNet  Google Scholar 

  • -. 2002. The Use of Cubic Equations in Islamic Art and Architecture. Pp. 165–179 in Nexus IV: Architecture and Mathematics, K. Williams and J. F. Rodrigues, eds. Fucecchio (Florence): Kim Williams Books.

    Google Scholar 

  • PUGACHENKOVA, G.A. 1986. ARCHITECTURE iv. Central Asia. Encyclopaedia Iranica, Online Edition. Available at: http://www.iranicaonline.org/articles/architecture-iv. Last accessed 6 April 2012.

    Google Scholar 

  • RASHED, R. 1994. The Development of Arabic Mathematics: Between Arithmetic and Algebra. Dordrecht and Boston: Kluwer.

    Book  MATH  Google Scholar 

  • -. 2005. Geometry and Dioptrics in Classical Islam. London: Al-Furqaan Islamic Heritage Association.

    Google Scholar 

  • REDFORD, S. 1991. The Alaeddin Mosque in Konya Reconsidered. Artibus Asiae 51: 54–74.

    Article  Google Scholar 

  • SALIBA, G. 2007. Islamic Science and the Making of the European Renaissance, Cambridge, MA: MIT Press.

    Google Scholar 

  • SALTZMAN, P. 2008. Quasi-Periodicity in Islamic Geometric Design. Pp. 153–168 in Nexus VII: Architecture and Mathematics, K. Williams, ed. Torino: Kim Williams Books.

    Google Scholar 

  • SEHERR-THOSS, S. P. and H. C. SEHERR-THOSS 1968. Design and Color in Islamic Architecture: Afghanistan, Iran, Turkey. Washington, D.C.: Smithsonian Institution.

    Google Scholar 

  • SEZGIN, F. ed. 1998. The School of Maragha and Its Achievements, Islamic Mathematics and Astronomy, vol. 50–51. Frankfurt: Publisher?.

    Google Scholar 

  • SHANI, R. 1996. A Monumental Manifestation of the Shi’ite Faith in Late Twelfth-Century Iran: The Case of the Gunbad-i ‘Alawiyan, Hamadan. Oxford Studies in Islamic Art XI. Oxford: Oxford University Press.

    Google Scholar 

  • MYRON BEMENT SMITH COLLECTION, Freer Gallery of Art and Arthur M. Sackler Gallery Archives, Smithsonian Institution, Washington DC. Gift of Katharine Dennis Smith, 1973–1985.

    Google Scholar 

  • STRONACH, D. and T. C. Young, Jr. 1966. Three Octagonal Seljuq Tomb Towers from Iran. Iran 4: 1–20.

    Article  Google Scholar 

  • VARDJAVAND, P. 1979. La Décourverte archéologique du complexe scientifique de l’observatoire de Maraqé. Pp. 527–536 in Akten des VII. Internationalen Kongresses für Iranische Kunst und Archäeologie (Munich, 7–10 September 1976). Berlin.

    Google Scholar 

  • WILBER, D. 1939. The Development of Mosaic Faience in Islamic Architecture in Iran. Ars Islamica VI: 16–47.

    Google Scholar 

  • -. 1969. The Architecture of Islamic Iran: The Il-Khanid Period (1955). Princeton: Princeton University Press

    Google Scholar 

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Bier, C. (2012). The Decagonal Tomb Tower at Maragha and Its Architectural Context: Lines of Mathematical Thought. In: Sarhangi, R. (eds) Persian Architecture and Mathematics. Nexus Network Journal. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0507-0_5

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