Bhāskara II - Revision history

Ramamurthy S: Internal links updated

2022-11-30T08:34:07Z

Internal links updated

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	Bhāskara II (c. 1114–1185)<ref>{{Cite web\|title=Bhāskara_II\|url=https://en.wikipedia.org/wiki/Bhāskara_II}}</ref>, also known as '''Bhāskarāchārya''' and as Bhāskara II to avoid confusion with [[~~Bhaskara I\|~~Bhāskara I]], was an Indian mathematician and astronomer. His main work Siddhānta-Śiromaṇi, (Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī, [[Algebra\|Bījagaṇita]], Grahagaṇita and Golādhyāya which are also sometimes considered four independent works. These four sections deal with arithmetic, [[algebra]], mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.		Bhāskara II (c. 1114–1185)<ref>{{Cite web\|title=Bhāskara_II\|url=https://en.wikipedia.org/wiki/Bhāskara_II}}</ref>, also known as '''Bhāskarāchārya''' and as Bhāskara II to avoid confusion with [[Bhāskara I]], was an Indian mathematician and astronomer. His main work Siddhānta-Śiromaṇi, (Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī, [[Algebra\|Bījagaṇita]], Grahagaṇita and Golādhyāya which are also sometimes considered four independent works. These four sections deal with arithmetic, [[algebra]], mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.

	Some of Bhāskara's contributions to mathematics include the following:		Some of Bhāskara's contributions to mathematics include the following:

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Indicwiki: 16 revisions imported from :alpha:Bhāskara_II

2022-11-29T03:32:19Z

16 revisions imported from alpha:Bhāskara_II

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alpha>Ramamurthy S: /* References */

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References

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			[[Category:Organic Articles English]]
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alpha>Abhishek: Abhishek moved page Bhaskara II to Bhāskara II

2022-11-28T09:39:34Z

Abhishek moved page Bhaskara II to Bhāskara II

← Older revision	Revision as of 15:09, 28 November 2022
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alpha>Ramamurthy S at 15:36, 27 October 2022

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	[[Līlāvatī]] (meaning a beautiful woman) is based on Arithmetic<ref>{{Cite web\|title=Bhāskara II\|url=https://www.booksfact.com/science/ancient-science/bhaskaracharya-greatest-mathematician-introduced-concept-infinity.html}}</ref>. It is believed that Bhāskara named this book after his daughter Līlāvatī. Many of the problems in this book are addressed to his daughter. For example “Oh Līlāvatī, intelligent girl, if you understand addition & subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 & 100, as well as [the remainder of] those when subtracted from 10000.” The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions were based on common objects like kings & elephants, which a common man could understand.		[[Līlāvatī]] (meaning a beautiful woman) is based on Arithmetic<ref>{{Cite web\|title=Bhāskara II\|url=https://www.booksfact.com/science/ancient-science/bhaskaracharya-greatest-mathematician-introduced-concept-infinity.html}}</ref>. It is believed that Bhāskara named this book after his daughter Līlāvatī. Many of the problems in this book are addressed to his daughter. For example “Oh Līlāvatī, intelligent girl, if you understand addition & subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 & 100, as well as [the remainder of] those when subtracted from 10000.” The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions were based on common objects like kings & elephants, which a common man could understand.
	* Solutions of [[Indeterminate Quadratic Equation\|indeterminate quadratic equations]] (of the type ''ax''<sup>2</sup> + ''b'' = ''y''<sup>2</sup>).		* Solutions of [[Indeterminate Quadratic Equation\|indeterminate quadratic equations]] (of the type ''ax''<sup>2</sup> + ''b'' = ''y''<sup>2</sup>).<ref>{{Cite web\|title=Bhāskara II\|url=https://www.newworldencyclopedia.org/entry/Bh%C4%81skara_II}}</ref>
	* The first general method for finding the solutions of the problem ''x''<sup>2</sup> − ''ny''<sup>2</sup> = 1 (so-called "Pell's equation") was given by Bhāskara II.		* The first general method for finding the solutions of the problem ''x''<sup>2</sup> − ''ny''<sup>2</sup> = 1 (so-called "Pell's equation") was given by Bhāskara II.
	* Preliminary concept of mathematical analysis.		* Preliminary concept of mathematical analysis.

alpha>Ramamurthy S at 15:27, 27 October 2022

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	* Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.		* Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.
	* Calculated the derivatives of trigonometric functions and formulae.		* Calculated the derivatives of trigonometric functions and formulae.
	* In ''Siddhānta-Śiromaṇi'', Bhāskara developed spherical trigonometry along with a number of other trigonometric results.		* In ''Siddhānta-Śiromaṇi'', Bhāskara developed spherical trigonometry along with a number of other trigonometric results<ref>{{Cite web\|title=Bhaskara’s knowledge of trigonometry\|url=https://speak2world.wordpress.com/2014/10/13/bhaskaras-knowledge-of-trigonometry/}}</ref>.
	The [[Siddhānta Śiromaṇi\|''Siddhānta'' ''Śiromaṇi'']] (written in 1150) demonstrates Bhāskara 's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry, along with other interesting trigonometrical results. In particular Bhāskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhāskara , results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin(a+b) and sin(a-b).		The [[Siddhānta Śiromaṇi\|''Siddhānta'' ''Śiromaṇi'']] (written in 1150) demonstrates Bhāskara 's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry, along with other interesting trigonometrical results. In particular Bhāskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhāskara , results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin(a+b) and sin(a-b).
	== See Also ==		== See Also ==

alpha>Ramamurthy S: Internal link added

2022-10-14T07:48:10Z

Internal link added

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	Bhāskara II (c. 1114–1185)<ref>{{Cite web\|title=Bhāskara_II\|url=https://en.wikipedia.org/wiki/Bhāskara_II}}</ref>, also known as '''Bhāskarāchārya''' and as Bhāskara II to avoid confusion with [[Bhaskara I\|Bhāskara I]], was an Indian mathematician and astronomer. His main work Siddhānta-Śiromaṇi, (Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya which are also sometimes considered four independent works. These four sections deal with arithmetic, [[algebra]], mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.		Bhāskara II (c. 1114–1185)<ref>{{Cite web\|title=Bhāskara_II\|url=https://en.wikipedia.org/wiki/Bhāskara_II}}</ref>, also known as '''Bhāskarāchārya''' and as Bhāskara II to avoid confusion with [[Bhaskara I\|Bhāskara I]], was an Indian mathematician and astronomer. His main work Siddhānta-Śiromaṇi, (Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī, [[Algebra\|Bījagaṇita]], Grahagaṇita and Golādhyāya which are also sometimes considered four independent works. These four sections deal with arithmetic, [[algebra]], mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.

	Some of Bhāskara's contributions to mathematics include the following:		Some of Bhāskara's contributions to mathematics include the following:

alpha>Ramamurthy S: Internal link added

2022-10-12T14:50:03Z

Internal link added

← Older revision		Revision as of 20:20, 12 October 2022
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	* Calculated the derivatives of trigonometric functions and formulae.		* Calculated the derivatives of trigonometric functions and formulae.
	* In ''Siddhānta-Śiromaṇi'', Bhāskara developed spherical trigonometry along with a number of other trigonometric results.		* In ''Siddhānta-Śiromaṇi'', Bhāskara developed spherical trigonometry along with a number of other trigonometric results.
	The ''Siddhānta'' ''Śiromaṇi'' (written in 1150) demonstrates Bhāskara 's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry, along with other interesting trigonometrical results. In particular Bhāskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhāskara , results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin(a+b) and sin(a-b).		The [[Siddhānta Śiromaṇi\|''Siddhānta'' ''Śiromaṇi'']] (written in 1150) demonstrates Bhāskara 's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry, along with other interesting trigonometrical results. In particular Bhāskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhāskara , results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for sin(a+b) and sin(a-b).
	== See Also ==		== See Also ==

alpha>Ramamurthy S: Internal link added

2022-10-12T14:48:35Z

Internal link added

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	* In ''Līlāvatī'', solutions of quadratic, cubic and quartic indeterminate equations are explained.		* In ''Līlāvatī'', solutions of quadratic, cubic and quartic indeterminate equations are explained.

	Līlāvatī (meaning a beautiful woman) is based on Arithmetic<ref>{{Cite web\|title=Bhāskara II\|url=https://www.booksfact.com/science/ancient-science/bhaskaracharya-greatest-mathematician-introduced-concept-infinity.html}}</ref>. It is believed that Bhāskara named this book after his daughter Līlāvatī. Many of the problems in this book are addressed to his daughter. For example “Oh Līlāvatī, intelligent girl, if you understand addition & subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 & 100, as well as [the remainder of] those when subtracted from 10000.” The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions were based on common objects like kings & elephants, which a common man could understand.		[[Līlāvatī]] (meaning a beautiful woman) is based on Arithmetic<ref>{{Cite web\|title=Bhāskara II\|url=https://www.booksfact.com/science/ancient-science/bhaskaracharya-greatest-mathematician-introduced-concept-infinity.html}}</ref>. It is believed that Bhāskara named this book after his daughter Līlāvatī. Many of the problems in this book are addressed to his daughter. For example “Oh Līlāvatī, intelligent girl, if you understand addition & subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 & 100, as well as [the remainder of] those when subtracted from 10000.” The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions were based on common objects like kings & elephants, which a common man could understand.
	* Solutions of [[Indeterminate Quadratic Equation\|indeterminate quadratic equations]] (of the type ''ax''<sup>2</sup> + ''b'' = ''y''<sup>2</sup>).		* Solutions of [[Indeterminate Quadratic Equation\|indeterminate quadratic equations]] (of the type ''ax''<sup>2</sup> + ''b'' = ''y''<sup>2</sup>).
	* The first general method for finding the solutions of the problem ''x''<sup>2</sup> − ''ny''<sup>2</sup> = 1 (so-called "Pell's equation") was given by Bhāskara II.		* The first general method for finding the solutions of the problem ''x''<sup>2</sup> − ''ny''<sup>2</sup> = 1 (so-called "Pell's equation") was given by Bhāskara II.