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By T.K Puttaswamy

Mathematics in India has an extended and ambitious heritage. offered in chronological order, this ebook discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic interval (800 B.C.) to the 17th Century of the Christian period. those contributions diversity around the fields of Algebra, Geometry and Trigonometry. The booklet provides the discussions in a chronological order, overlaying the entire contributions of 1 Pre-Modern Indian Mathematician to the subsequent. It starts with an summary and precis of earlier paintings performed in this topic prior to exploring particular contributions in exemplary technical aspect. This publication presents a accomplished exam of pre-Modern Indian mathematical contributions that would be useful to mathematicians and mathematical historians.

  • Contains greater than one hundred sixty unique Sanskrit verses with English translations giving historic context to the contributions
  • Presents many of the proofs step-by-step to assist readers understand
  • Uses glossy, present notations and emblems to boost the calculations and proofs

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9396 % 97  5 16 % 2 2 5 7 6 2 pffiffiffiffiffi . 61 %   5 47 5 7:833::: 7 5 6 6 We also have pffiffiffi pffiffiffi 577 1 1 1 2 % 11 1 2 . 2% 3 3 Á 4 3 Á 4 Á 34 408 The Sulvasutras 35 pffiffiffi The very fact that pffiffiffithree different values of 2 were given shows that the ancient Indians knew that 2 could not be determined. This in turn leads to the concept of irrational numbers. From this, it is very clear that Indians were the first people to use irrational numbers. W. George Cantor (1829À1920), and Karl Theodor Wilhelm Weierstrass (1815À1897).

18. 19. 20. 21. 22. 23. 24. n k3 k4 k1 1 k2 1 k3 1 k4 17 9 22 9 34 9 41 9 25 9 46 9 1 9 1 65 18 55 18 31 18 17 18 89 36 5 36 167 36 15 4 5 12 67 36 13 12 47 18 5 18 35 9 10 3 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 15 2 14 9 26 9 11 3 17 9 38 9 1 9 2 3 2 25 9 1 14 9 17 9 25 9 11 9 21 4 169 36 157 36 125 36 x y z w 4 49 17 130 4 64 22 110 4 100 34 62 4 121 41 34 5 81 25 89 5 144 46 5 7 25 1 167 7 49 9 135 7 64 14 115 7 100 26 67 7 121 33 39 8 81 17 94 8 144 38 10 10 49 1 140 10 64 6 120 10 100 18 72 10 121 25 44 1 1 9 189 1 16 14 169 1 25 17 157 1 49 25 125 (Continued) 52 Mathematical Achievements of Pre-modern Indian Mathematicians (Continued) Solution No.

Now, from (A) z5 p½qfð15=2Þ 2 ðk1 1 k2 Þg 2 f200 2 mk1 2 nk2 gŠ q2p Suppose we choose (m, n, p, q) 5 (4, n, 9, 36), where n 6¼ 4, n 6¼ 9, and n 6¼ 36. y 5 n. x 5 4 Then, z5 34 2 32 1 n 2 1 n 5 is an integer $ 0 3 3 (1) Let n 5 1; then y 5 n 5 1 and z 5 211 3 5 51 3 3 w 5 200 2 x 2 y 2 z 5 200 2 4 2 1 2 1 5 194 Then, (x, y, z, w) 5 (4, 1, 1, 194) is a solution. y 5 16; z5 2 1 n 2 1 16 18 5 5 56 3 3 3 w 5 200 2 x 2 y 2 z 5 200 2 4 2 16 2 6 5 174 Then, (x, y, z, w) 5 (4, 16, 6, 174) is a solution.

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