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ARTICLE : Mathematics in ancient India
Contributions of Indian Mathematicians:
1. Solution of quadratic equations: Source: Lilavati
2. Pythagoras principle:
3. Algorithms, Arithmetic Series, Goemertic Series,
Cube Series, Square Series, Mathematical Induction
(Refer: Aryabhattiyam by Aryabhatta)
4. Zero and decimal system.
5. Permutations and Combinations [P(n,r] and C[n,r]]:
Refer Lilavati by Bhaskar.
6. Ayangaghosh: Binomial Theorem: (Robert Burrow, a British
person, who was in India during the 17th and 18th centuries
writes: "As far as the issue of Binomial Principle is concerned
the manuscript enclosed with this letter clearly shows that
the Hindus were well versed with it."
7. Trigonometry: (trikon-miti in Samskrit, meaning: The measure
of triangles).
a) SIne and Cosines: Padmakar Dwivedi's treatises Ganita
Kaumidi, and Laghu-manasa.
b) Manjula (432 AD) uses concepts like: (Sin[x-dx]-SIn[x])/dx = 1,
if dx approaches zero. Herein we see the roots of modern
calculus, which was later developed by Newton and Leibnitz.
c) C.M Whish, an English, writes in 1835: "The invention of
the series of Pi, Sine, and Cosine, had occured in India,
much before the times of Newton and Leibnitz. The actual
credit for the development of these series should go to
the Indians only. (Refer: T. A. Saraswat's Commentary on
'Ganita Kaumudi by Padmakar Dwivedi').
--
Nachiketa Tiwari
