Chitrabhanu (mathematician)

Chitrabhanu (IAST: Citrabhānu; fl. 16th century) was a mathematician of the Kerala school and a student of Nilakantha Somayaji. 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.^[1][2]

Contributions

He gave integer solutions to 21 types of systems of two simultaneous Diophantine equations in two unknowns.^[1] These types are all the possible pairs of equations of the following seven forms:^[3]

$\ x + y = a, x - y = b, xy = c, x^2 + y^2 = d, x^2 - y^2 = e, x^3 + y^3 = f, x^3 - y^3 = g$

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

1. Joseph, George Gheverghese (2009), A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, SAGE Publications India, p. 21, ISBN 9788132104810.
2. Plofker, Kim (2009). Mathematics in India. Princeton: Princeton University Press. pp. 220, 319, 323. ISBN 9780691120676. Retrieved 7 April 2016.
3. 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.