Abstract :

Despite the stylistic and structural significance of discontinuous double-shell domes in architectural heritage, limited scholarly attention has been devoted to their geometric foundations. This case-based study investigates the relationship between theoretical and practical geometry in the design and construction of discontinuous double-shell domes. The research seeks to answer two main questions: (1) What is the connection between theoretical and applied geometry in the shaping of such domes? (2) What are the key factors influencing their design and construction process? The study begins with a review of the theoretical foundations of geometry in architecture, followed by an analysis of a selected case study to trace the application of geometric and proportional principles derived from the theoretical phase. Through this analysis, the underlying geometric logic of the dome’s formation is decoded. The results reveal that the dome was designed based on a premeditated geometric system involving fundamental shapes—square, circle, and pentagon—with proportions governed by the golden ratio. These proportions are consistently manifested in the plan, section, and elevation. The study contributes to the understanding of traditional geometric practices and their potential application in the conservation of historical domed structures as well as the design of contemporary shell architecture.

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Keywords :

Architectural Geometry, Double-Shell Dome, Geometric Design, Indigenous Knowledge, Practical Geometry, Proportions, Structural analysis, Theoretical Geometry., Traditional Architecture

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References :

1. Askarov, S. (2003). Splendour of Bukhara. Archive of San’at magazine, 44. Retrieved from http://www.sanat.orexca.com/eng/4-03/history_art2.shtml
2. Creswell, K. A. C. (1958). A short account of the Early Muslim architecture II. Oxford: Clarendon Press.
3. Dold-Samplonius, Y. (1992). The 15th century Timurid mathematician Ghiyath al-Din Jamshid al-Kashi and his computation of the Qubba. In S. S. Demidov et al. (Eds.), Amphora: Festschrift for Hans Wussing on the occasion of his 65th birthday (pp. 171–181). Basel, Boston, Berlin.
4. Dold-Samplonius, Y. (2000). Calculation of arches and domes in 15th century Samarkand. Nexus Network Journal, 22(3), 45–55.
5. Farshad, M. (1977). On the shape of momentless tensionless masonry domes. Journal of Building and Environment, 12, 81–85.
6. Grabar, O. (1963). The Islamic dome: Some considerations. The Journal of the Society of Architectural Historians, 22(4), 191–198.
7. Grabar, O. (2006). Islamic art and beyond. United Kingdom: Variorum Press.
8. Grangler, A. (2004). Bukhara: The eastern dome of Islam. Stuttgart: Axel Menges Press.
9. Hejazi, M. M. (1997). Historical buildings of Iran: Their architecture and structure. Southampton: Computational Mechanics Publications.
10. Hejazi, M. M. (2003). Seismic vulnerability of Iranian historical domes. Journal of Earthquake Resistant Engineering Structures, 4, 157–165.
11. Huerta, S. (2006). Galileo was wrong: The geometrical design of masonry arches. Nexus Network Journal, 8(2), 25–52.
12. Hillenbrand, R. (1994). Islamic architecture: Form, function, and meaning. New York: Columbia University Press.
13. Hillenbrand, R. (1999). The Ilkhanids and Timurids. In Islamic art and architecture (pp. 196–202). London: Thames and Hudson.
14. Hoag, J. D. (2004). History of world architecture: Islamic architecture. Milan: Phaidon Press.
15. Hogendijk, J. P., & Sabra, A. I. (Eds.). (2003). The enterprise of the science in Islam: New perspectives. Cambridge: MIT Press.
16. Irfan, H. (2002). Sacred geometry of Islamic mosque. Islamonline-News Section. Retrieved from http://www.islamonline.net/English/Science/2002/07/article02.shtml
17. Katz, V. J. (Ed.). (2007). The mathematics of Egypt, Mesopotamia, China, India, and Islam: A source book. New Jersey: Princeton University Press.
18. Kennedy, E. S. (1960). A letter of Jamshid al-Kashi to his father: Scientific research at a fifteenth century court. Orientalia, Nova Series, 29, 191–213.
19. Mainstone, R. J. (2001). Vaults, domes, and curved membranes. In Developments on structural form (p. 124). London: Architectural Press.
20. Meinecke, M. (1985). Mamluk architecture, regional architectural traditions: Evolution and interrelations. Damas-zener Mitteilungen, 2, 163–175.
21. Michell, G. (Ed.). (1978). Architecture of the Islamic world: Its history and social meaning. New York: Thames and Hudson.
22. O’Connor, J. J., & Robertson, E. F. (1999). Abu Sahl Waijan ibn Rustam al-Quhi. In School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved from http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Quhi.html
23. O’Kane, B. (1998). Dome in Iranian architecture. In Iranian art and architecture. Retrieved from http://www.cais-soas.com/CAIS/Architecture/dome.htm
24. Özdural, A. (1995). Omar Khayyam, mathematicians, and “conversazioni” with artisans. Journal of the Society of Architectural Historians, 54(1), 54–71.
25. Özdural, A. (2000). Mathematics and arts: Connections between theory and practice in the medieval Islamic world. The Journal of Historia Mathematica, 27(2), 171–201.
26. Pope, A. U. (1971). Introducing Persian architecture. London: Oxford University Press.
27. Saud, R. (2003). Muslim architecture under Seljuk patronage (1038–1327). Foundation for Science, Technology, and Civilization (FSTC). Retrieved from http://www.muslimheritage.com/features/default.cfm?ArticleID=347
28. Seherr-Thoss, S. P. (1968). Design and color in Islamic architecture: Afghanistan, Iran, Turkey. Washington, D.C.: Smithsonian Institution Press.
29. Smith, E. B. (1971). The dome: A study in the history of ideas. New Jersey: Princeton Press.
30. Stierlin, H. (2002). Islamic art and architecture: From Isfahan to the Taj Mahal. London: Thames and Hudson.
31. Wilber, D. N. (1986). Me’māri-ye eslāmi-ye Irān dar dore-ye Ilkhānān (A. Faryar, Trans.). 2nd ed. Tehran: Scientific and Cultural Publishing Co.