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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Main Authors:	Ganikhodjaev, Nasir, Husain, Ahmad Hamidi
Format:	Conference or Workshop Item
Language:	English English English
Published:	American Institute of Physics 2018
Subjects:	QA Mathematics
Online Access:	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

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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 Conference or Workshop Item 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
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Husain, Ahmad Hamidi Al-Kāshī, the first scientist who introduced dynamical system
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.
format	Conference or Workshop Item
author	Ganikhodjaev, Nasir Husain, Ahmad Hamidi
author_facet	Ganikhodjaev, Nasir Husain, Ahmad Hamidi
author_sort	Ganikhodjaev, Nasir
title	Al-Kāshī, the first scientist who introduced dynamical system
title_short	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_sort	al-kāshī, the first scientist who introduced dynamical system
publisher	American Institute of Physics
publishDate	2018
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
first_indexed	2023-09-18T21:33:57Z
last_indexed	2023-09-18T21:33:57Z
_version_	1777412695595679744

Al-Kāshī, the first scientist who introduced dynamical system

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