Application of curve fitting and least squares method for investigating the geometry of Iranian arches

Document Type : Research Paper

Author

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

References

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History

  • Receive Date: 01 March 2015
  • Revise Date: 30 December 2017
  • Accept Date: 01 January 2018
  • Publish Date: 22 May 2018

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