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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> | '''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 | ||
| Line 13: | Line 13: | ||
| 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> | ||
Latest revision as of 23:31, 28 November 2021
Chitrabhanu (IAST: Citrabhānu; fl. 16th century) was a mathematician of the Kerala school and a student of Nilakantha Somayaji. He was a Nambudiri brahmin from the town of Covvaram near present day Trissur.[1] He is noted for a karaṇa, a concise astronomical manual, dated to 1530, an algebraic treatise, and a commentary on a poetic text. Nilakantha and he were both teachers of Shankara Variyar.[2][3]
Contributions[edit | edit source]
He gave integer solutions to 21 types of systems of two simultaneous Diophantine equations in two unknowns.[2] These types are all the possible pairs of equations of the following seven forms:[4]
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[edit | edit source]
- ↑ Joseph, George Gheverghese (10 December 2009). A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact. ISBN 9788132104810.
- ↑ 2.0 2.1 Joseph, George Gheverghese (2009), A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, SAGE Publications India, p. 21, ISBN 9788132104810.
- ↑ Plofker, Kim (2009). Mathematics in India. Princeton: Princeton University Press. pp. 220, 319, 323. ISBN 9780691120676.
- ↑ Hayashi, Takao; Kusuba, Takanori (1998), "Twenty-one algebraic normal forms of Citrabhānu", Historia Mathematica, 25 (1): 1–21, doi:10.1006/hmat.1997.2171, MR 1613702.
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