Al-Kāshī, the first scientist who introduced dynamical system
In 15th century, two renowned mathematicians, Ghiyāth al-Dīn Jamshīd Mas’ūd al-Kāshī (also known as Jamshīd Kāshānī; d. 1429) and his patron, Mīrzā Muhammad Tāraghay bin Shāhrukh (well known as Ulugh Beg; d. 1449) were able to calculate the sine and chord of one-third of an angle. With this, they...
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| Format: | Proceeding Paper |
| Language: | English English English |
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American Institute of Physics
2018
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| Online Access: | http://irep.iium.edu.my/66204/ http://irep.iium.edu.my/66204/1/Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical%20system.pdf http://irep.iium.edu.my/66204/7/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical_scopus.pdf http://irep.iium.edu.my/66204/13/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20_wos.pdf |
| _version_ | 1848786530388148224 |
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| author | Ganikhodjaev, Nasir Husain, Ahmad Hamidi |
| author_facet | Ganikhodjaev, Nasir Husain, Ahmad Hamidi |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | In 15th century, two renowned mathematicians, Ghiyāth al-Dīn Jamshīd Mas’ūd al-Kāshī (also known as
Jamshīd Kāshānī; d. 1429) and his patron, Mīrzā Muhammad Tāraghay bin Shāhrukh (well known as Ulugh Beg; d.
1449) were able to calculate the sine and chord of one-third of an angle. With this, they successfully computed sine 1° to
17 correct decimal digits (ten correct sexagesimal places) by the invention of ingenious converging iteration algorithm.
The iteration algorithm suggested by Al-Kāshī one can consider as pioneering dynamical system and Al-Kāshī himself
can be considered as the initiator, pioneer of the theory of dynamical systems. In this paper we revise Al-Kāshī’s work on
this computation of sine 1° using modern theory of dynamical systems. The main reference for this computation will be
based on A Study of Risāla al-Watar wa’l Jaib (“The Treatise on the Chord and Sine”), written by Mohammad K.
Azarian. In the end, we discuss the significance of this revision in the Islamic point of view. |
| first_indexed | 2025-11-14T17:10:30Z |
| format | Proceeding Paper |
| id | iium-66204 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English English |
| last_indexed | 2025-11-14T17:10:30Z |
| publishDate | 2018 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-662042019-08-08T14:54:58Z http://irep.iium.edu.my/66204/ Al-Kāshī, the first scientist who introduced dynamical system Ganikhodjaev, Nasir Husain, Ahmad Hamidi QA Mathematics In 15th century, two renowned mathematicians, Ghiyāth al-Dīn Jamshīd Mas’ūd al-Kāshī (also known as Jamshīd Kāshānī; d. 1429) and his patron, Mīrzā Muhammad Tāraghay bin Shāhrukh (well known as Ulugh Beg; d. 1449) were able to calculate the sine and chord of one-third of an angle. With this, they successfully computed sine 1° to 17 correct decimal digits (ten correct sexagesimal places) by the invention of ingenious converging iteration algorithm. The iteration algorithm suggested by Al-Kāshī one can consider as pioneering dynamical system and Al-Kāshī himself can be considered as the initiator, pioneer of the theory of dynamical systems. In this paper we revise Al-Kāshī’s work on this computation of sine 1° using modern theory of dynamical systems. The main reference for this computation will be based on A Study of Risāla al-Watar wa’l Jaib (“The Treatise on the Chord and Sine”), written by Mohammad K. Azarian. In the end, we discuss the significance of this revision in the Islamic point of view. American Institute of Physics 2018-06-28 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/66204/1/Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical%20system.pdf application/pdf en http://irep.iium.edu.my/66204/7/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical_scopus.pdf application/pdf en http://irep.iium.edu.my/66204/13/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20_wos.pdf Ganikhodjaev, Nasir and Husain, Ahmad Hamidi (2018) Al-Kāshī, the first scientist who introduced dynamical system. In: 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017, 27 - 29 August 2017, SKSM 2017; Kuantan, Pahang;. https://aip.scitation.org/doi/pdf/10.1063/1.5041643?class=pdf 10.1063/1.5041643 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Husain, Ahmad Hamidi Al-Kāshī, the first scientist who introduced dynamical system |
| title | Al-Kāshī, the first scientist who introduced dynamical system |
| title_full | Al-Kāshī, the first scientist who introduced dynamical system |
| title_fullStr | Al-Kāshī, the first scientist who introduced dynamical system |
| title_full_unstemmed | Al-Kāshī, the first scientist who introduced dynamical system |
| title_short | Al-Kāshī, the first scientist who introduced dynamical system |
| title_sort | al-kāshī, the first scientist who introduced dynamical system |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/66204/ http://irep.iium.edu.my/66204/ http://irep.iium.edu.my/66204/ http://irep.iium.edu.my/66204/1/Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical%20system.pdf http://irep.iium.edu.my/66204/7/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20who%20introduced%20dynamical_scopus.pdf http://irep.iium.edu.my/66204/13/66204_Al-K%C4%81sh%C4%AB%2C%20the%20first%20scientist%20_wos.pdf |