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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>{{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><br />
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==Contributions==<br />
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<br />
| last1 = Hayashi | first1 = Takao<br />
| last2 = Kusuba | first2 = Takanori<br />
| doi = 10.1006/hmat.1997.2171<br />
| issue = 1<br />
| journal = [[Historia Mathematica]]<br />
| mr = 1613702<br />
| pages = 1–21<br />
| title = Twenty-one algebraic normal forms of Citrabhānu<br />
| volume = 25<br />
| year = 1998| doi-access = free<br />
}}.</ref><br />
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<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><br />
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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.<br />
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==References==<br />
{{reflist}}<br />
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{{Scientific Research in Kerala |state=collapsed}}<br />
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[[Category:Kerala school of astronomy and mathematics]]<br />
[[Category:15th-century births]]<br />
[[Category:16th-century deaths]]<br />
[[Category:16th-century Indian mathematicians]]<br />
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