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Application of curve fitting and least squares method for investigating the geometry of Iranian arches | ||
| نشریه ریاضی و جامعه | ||
| Article 5, Volume 3, Issue 1, March 2018, Pages 41-53 PDF (1.96 M) | ||
| Document Type: Research Paper | ||
| DOI: 10.22108/msci.2018.24929.1130 | ||
| Author | ||
| Farzin Izadpanah* | ||
| Shahid Bahonar university of Kerman | ||
| Abstract | ||
| There are different perspectives regarding the use of conic sections in the structures of historical domes. This debate is also prevalent in Iranian architecture, shaping part of the history of global architectural studies. Some argue for the use of catenary curves, which represent the most significant competitor to conic sections in the history of arch geometry studies. Part of the research into this hypothesis is a historical examination, while another part involves a mathematical analysis of the arch curves. In the architectural literature, the investigation of arch curves has been carried out by plotting curves on the arch and visually comparing them. However, the author seeks a more precise method for examining this issue. In this paper, curve fitting using a matrix method is employed for examination. To compare the error rates in the fitting of the desired curves, the least squares method is highlighted. For demonstration purposes, a selected arch from the Elam period is examined and compared with catenary and conic section curves.The author recommends this method as a suitable approach for studying historical graphical documents. | ||
| Keywords | ||
| Curve Fitting; Least Squares Method; Iranian Arch Geometry; Catenary Curve; Conic Sections | ||
| References | ||
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[1] L. Abolghasmi, The Islamic art and architecture of Iran in memory, Tehran, 2005. [2] M. K. Pirnia, A research in the past architecture of Iran, Tehran, 2010 [3] H. Zumar shady, Arch in architecture of Iran, Keyhan Press, 1983. [4] J. Ladyman, Understanding philosophy of science, H. Karami, Hekmat Publication, 2011. [5] D. Arnold, Building in Egypt, Pharaonic stone masonry, Oxford, Oxford University Press, 1991. [6] R. Besenval, Technologie de la voûtedansl’OrientAncien, 2 vols, Paris: Editions Recherchesur les Civilisations, 1984. [7] Ph. Block Etal, As Hangs the Flexible Line :Equilibrium of Masonry Arches, Nexu. Netw. J., 8, (2006) 13–24. [8] S. L. Cambell and J. R. Meyer, Generalized Inverses of Linear Transformations, London, Pitman Publishing Limited, 1979. [9] G. Daressy, Une trace Egyptienneconservéed’unevoûteelliptique, Annales du service des antiquités de l’Egypte, 8 (1907) 234–241. [10] S. Huerta, Oval Domes: History, Geometry and Mechanics, Nexu. Netw. J., 9 (2007) 211–248. [11] D. Huylebrouck, Curve Fitting in Architecture, Nexu. Netw. J., 9 (2007) 559–70. [12] F. Izadpanah, A Suspension: Using Conic Sections in Persian Arch Structures, J. of Eng. and Arch., 3 (2015) 160–168 [13] G. Necipoglo, The Topkapi Scroll-Geometry and Ornament in Islamic Architecture With an Essay on the Geometry of the Muqrnas by Mohammad Alasad, Los Angeles, The Getty Centre of the History of Art and Humanities, 1995. [14] M. Salehi, Sepultures etcoutumesfuneraires au II millenaire a Suse, Haft tepe et TchogaZanbil Memoire de maitrise,Universite de Paris I, 1975/1976. [15] S. Tolstov and B. Vajnberg, Kojkrylgan t.lh.e., 5, 1967. | ||
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