Chitrabhanu (mathematician) - Revision history

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	'''Chitrabhanu''' ({{IAST3\|Citrabhānu}}; {{flourished\|16th century}}) was a mathematician of the [[Kerala school of astronomy and mathematics\|Kerala school]] and a student of [[Nilakantha Somayaji]]. He was a [[Nambudiri]] brahmin from the town of Covvaram near present day [[Trissur]].<ref>[https://books.google.com~~.au~~/books?id=rNKGAwAAQBAJ&pg=PA21~~&redir_esc~~=~~y&hl=en#v=onepage&q&f=false https~~:~~//books.google.com.au/books?id~~=~~rNKGAwAAQBAJ&pg~~=~~PA21&redir_esc~~=~~y&hl~~=~~en#v=onepage&q&f=false]~~</ref> He is noted for a {{IAST\|karaṇa}}, a concise astronomical manual, dated to 1530, an [[algebra]]ic treatise, and a commentary on a poetic text. [[Nilakantha Somayaji\|Nilakantha]] and he were both teachers of [[Shankara Variyar]].<ref name="ggj" /><ref name="plofker">{{cite book\|last1=Plofker\|first1=Kim\|title=Mathematics in India\|title-link=Mathematics in India\|date=2009\|publisher=[[Princeton University Press]]\|location=Princeton\|isbn=9780691120676\|pages=[https://books.google.com/books?id=DHvThPNp9yMC&pg=PA220 220, 319, 323]}}</ref>		'''Chitrabhanu''' ({{IAST3\|Citrabhānu}}; {{flourished\|16th century}}) was a mathematician of the [[Kerala school of astronomy and mathematics\|Kerala school]] and a student of [[Nilakantha Somayaji]]. He was a [[Nambudiri]] brahmin from the town of Covvaram near present day [[Trissur]].<ref>{{Cite book\|url=https://books.google.com/books?id=rNKGAwAAQBAJ&pg=PA21\|title = A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact\|isbn = 9788132104810\|last1 = Joseph\|first1 = George Gheverghese\|date = 10 December 2009}}</ref> He is noted for a {{IAST\|karaṇa}}, a concise astronomical manual, dated to 1530, an [[algebra]]ic treatise, and a commentary on a poetic text. [[Nilakantha Somayaji\|Nilakantha]] and he were both teachers of [[Shankara Variyar]].<ref name="ggj" /><ref name="plofker">{{cite book\|last1=Plofker\|first1=Kim\|title=Mathematics in India\|title-link=Mathematics in India (book)\|date=2009\|publisher=[[Princeton University Press]]\|location=Princeton\|isbn=9780691120676\|pages=[https://books.google.com/books?id=DHvThPNp9yMC&pg=PA220 220, 319, 323]}}</ref>

	==Contributions==		==Contributions==
	He gave integer solutions to 21 types of systems of two [[simultaneous equation\|simultaneous]] [[Diophantine equation\|Diophantine]] equations in two unknowns.<ref name="ggj">{{citation\|title=A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact\|first=George Gheverghese\|last=Joseph\|publisher=SAGE Publications India\|year=2009\|isbn=9788132104810\|page=21\|url=https://books.google.com/?id=rNKGAwAAQBAJ&pg=PA21}}.</ref> These types are all the possible pairs of equations of the following seven forms:<ref>{{citation		He gave integer solutions to 21 types of systems of two [[simultaneous equation\|simultaneous]] [[Diophantine equation\|Diophantine]] equations in two unknowns.<ref name="ggj">{{citation\|title=A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact\|first=George Gheverghese\|last=Joseph\|publisher=SAGE Publications India\|year=2009\|isbn=9788132104810\|page=21\|url=https://books.google.com/books?id=rNKGAwAAQBAJ&pg=PA21}}.</ref> These types are all the possible pairs of equations of the following seven forms:<ref>{{citation
	\| last1 = Hayashi \| first1 = Takao		\| last1 = Hayashi \| first1 = Takao
	\| last2 = Kusuba \| first2 = Takanori		\| last2 = Kusuba \| first2 = Takanori

imported>OAbot: Open access bot: doi added to citation with #oabot.

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	\| title = Twenty-one algebraic normal forms of Citrabhānu		\| title = Twenty-one algebraic normal forms of Citrabhānu
	\| volume = 25		\| volume = 25
	\| year = 1998}}.</ref>		\| year = 1998\| doi-access = free
			}}.</ref>

	<math>\ x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g</math>		<math>\ x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g</math>

>David Eppstein: fix

2020-12-28T20:08:34Z

fix

New page

{{Use dmy dates|date=July 2019}}
'''Chitrabhanu''' ({{IAST3|Citrabhānu}}; {{flourished|16th century}}) was a mathematician of the [[Kerala school of astronomy and mathematics|Kerala school]] and a student of [[Nilakantha Somayaji]]. He was a [[Nambudiri]] brahmin from the town of Covvaram near present day [[Trissur]].<ref>[https://books.google.com.au/books?id=rNKGAwAAQBAJ&pg=PA21&redir_esc=y&hl=en#v=onepage&q&f=false https://books.google.com.au/books?id=rNKGAwAAQBAJ&pg=PA21&redir_esc=y&hl=en#v=onepage&q&f=false]</ref> He is noted for a {{IAST|karaṇa}}, a concise astronomical manual, dated to 1530, an [[algebra]]ic treatise, and a commentary on a poetic text. [[Nilakantha Somayaji|Nilakantha]] and he were both teachers of [[Shankara Variyar]].<ref name="ggj" /><ref name="plofker">{{cite book|last1=Plofker|first1=Kim|title=Mathematics in India|title-link=Mathematics in India|date=2009|publisher=[[Princeton University Press]]|location=Princeton|isbn=9780691120676|pages=[https://books.google.com/books?id=DHvThPNp9yMC&pg=PA220 220, 319, 323]}}</ref>

==Contributions==
He gave integer solutions to 21 types of systems of two [[simultaneous equation|simultaneous]] [[Diophantine equation|Diophantine]] equations in two unknowns.<ref name="ggj">{{citation|title=A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact|first=George Gheverghese|last=Joseph|publisher=SAGE Publications India|year=2009|isbn=9788132104810|page=21|url=https://books.google.com/?id=rNKGAwAAQBAJ&pg=PA21}}.</ref> These types are all the possible pairs of equations of the following seven forms:<ref>{{citation
| last1 = Hayashi | first1 = Takao
| last2 = Kusuba | first2 = Takanori
| doi = 10.1006/hmat.1997.2171
| issue = 1
| journal = [[Historia Mathematica]]
| mr = 1613702
| pages = 1–21
| title = Twenty-one algebraic normal forms of Citrabhānu
| volume = 25
| year = 1998}}.</ref>

<math>\ x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g</math>

For each case, Chitrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric.

==References==
{{reflist}}

{{Scientific Research in Kerala |state=collapsed}}
{{Authority control}}

[[Category:Kerala school of astronomy and mathematics]]
[[Category:15th-century births]]
[[Category:16th-century deaths]]
[[Category:16th-century Indian mathematicians]]

{{India-scientist-stub}}
{{asia-mathematician-stub}}