T.S. Bhanumurthy
New Age International Pvt Ltd Publishers | 2009 - 2ª edição | 270 páginas | djvu | 2,2 Mb
Suitable for students and teachers of mathematics, this book deals with the historical continuity of Indian Mathematics, starting from the Sulba Sutras of the Vedas up to the 17th century.
CONTENTS Preface to the Second Edition v
Preface to the First Edition vii
I. INTEGERS 1
1. The Decimal Place Value System 1
2. Divisibility 5
3. Greatest Common Divisor and Least Common Multiple
4. Simple Continued Fractions 20
5. The Euler
7. Congruences 40
II. TOPICS IN SRI BHARATHI KRISHNA THIRTHA'S VEDIC MATHEMATICS
1. Some Questions of Divisibility 59
2. Recurring Decimals 65
3. Square 75
4. Square Root 82
5. Cube 88
6. Cube Root 90
III. THE BRAHMAGUPrA-BHASKARA EQUATION 103
1. Lemmas of BRAHMAGUPTA 103
2. Examples 106
3. CHAKRAVALA Method of BHASKARA 108
4. Historical Remarks 120
5. Continued Fractions 121
6. Remarks on 1t 135
7. Theorem of BHASKARA 141
IV. SELECTED TOPICS IN GEOMETRY 155
1. Geometry in the Sulba SiItras 155
2. The Triangle 168
3. The Cyclic Quadrilateral 176
4. The Circle 182
APPENDIX 195
SUPPLEMENT-I 213
BKT Algorithms 213
1. Multiplication and Division 213
SUPPLEMENT-II 222
Some Remarks on Pell's Equation and Bhaskaras Chakravala Method 222
1. Introduction 222
2. The Bhaskara Coefficients m').. and h').. for Ji5 223
SUPPLEMENT-III 232
1. Polynomial Rings 232
2. Statement of the Fundamental Theorem on
Symmetric Functions 234
3. The Field Q of Algebraic Numbers 235
4. Taylor Expansion for Polynomials 237
5. Transcendence of e and 1t 240
6. Dirichlet's Approximation Theorem-Siegel's Lemma 251
7. Miscellaneous Theorem and Examples 253
REFERENCES 259
SUGGESTED READINGS 259
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