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Re: ARTICLE : Mathematics in ancient India
N. Tiwari (ntiwari@rs3.esm.vt.edu) wrote:
: N. Tiwari (ntiwari@rs3.esm.vt.edu) wrote:
: : 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.
: Thanks for pointing out the error.
: It should have been (Sin[x+dx]-Sin[x])/dx=1
A blunder followed by another blunder. The
correct thing should be:
(Sin[x+dx]-Sin[x])/dx=Cos[x]
in the limiting sense.
: : 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
: : --
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: --
: Nachiketa Tiwari
: --
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--
Nachiketa Tiwari
