Index Page No. Part - 1 1 1. Mathematics in Vedas 3 2. Additions 6 3. Subtractions 9 4. Multiplications-1 12 5. Multiplications-2 15 6. Complements 16 7. Multiplications-3 17 8. Multiplications-4 23 9. Multiplications-5 30 10. Multiplications-6 37 11. Multiplications-7 40 12. Multiplications-8 42 13. Multiplications-9 47 Part - 2 59 14. Vinculam Numbers 61 15. Cube Values-1 74 16. Cube Values-2 78 17. Divisions-1 84 18. Symmetry in the Quotient 89 19. Divisions-2 91 20. Divisions-3 93 21. Divisions-4 97 22. Multiplications-10 102 Part - 3 107 23. Decimal number System in Vedas 109 24. Measures of numbers 117 25. Multiplications-11 121 26. Multiplications-12 127 27. Multiplications-13 132 28. Multiplications-14 134 29. Multiplications-15 136 30. Multiplications-16 138 31. Multiplications-17 140 32. Multiplications -18 144 33. Multiplications-19 147 iv
34. Multiplications-20 149 35. Multiplications-21 152 36. Akshahridayam 153 37. Positional weightage system 154 38. Infinity 156 39. AC and HAL SYMBOLS 157 Part - 4 159 40. Methodology for Expressing Numbers in Sanskrit 161 41. Katapayadi System - 1 162 42. Katapayadi System - 2 164 43. Katapayadi System in Vedantasastra 169 44. Katapayadi System in Sangita Sastra 171 45. Magic Squares with Katapayadi Numbers 172 46. Magic Squares with katapayadi Numbers 175 47. Katapayadi System - 3 178 48. Number of Planetary Revolutions with Katapayadi System 181 49. Logic Behind the Naming of Weekdaya in Sanskrit 184 50. Vedic Numerical Codes / Algebraic Notation 189 51. Matrhematics in Chandas Sastra (Prosody) 210 Part - 5 213 52. Long term calender -1 215 53. Long term calender -2 220 54. Long term calender -3 231 55. Multiplications - Lilavati Ganitam 235 56. Method for validation of product of multiplication 244 57. About Bhaskaracharya 246 58. Divisions - 5 248 59. Prime Numbers 254 60. Reference to numbers like 19,29,39 and 49 in vedas 255 61. Digits & Numbers -their Characteristics -1 256 62. Mystic codes in our Philosophy 261 63. Digits & Numbers -their Characteristics -2 262 64. Divisibility 269 Part - 6 273 65. Divisions - 5 275 66. Divisions -6 278 67. Divisions -7 285 68. Divisions -8 286 v
69. Ancient Mathematicians of India 287 70. Some Contributions of Indian 289 Mathematicians 71. Squares - 1 292 72. Squares -2 293 73. Squares -3 301 74. Squares -4 305 75. Squares -5 309 76. Square Roots - 1 312 77. Square Roots - 2 314 78. Square Roots - 3 325 79. Square Roots - 4 331 80. Square Roots - 5 339 Part - 7 347 81. Cubes - 3 348 82. Cubes - 4 357 83. Cubes - 5 360 84. Cube Roots - 1 363 85. Cube Roots - 2 364 86. Cube Roots - 3 383 87. Cube Roots - 4 388 88. Cube Roots - 5 395 89. Fourth Order Roots 401 90. Fifth Order Roots - 1 402 91. Fifth Order Roots - 2 403 vi
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Introduction 1. Mathematics in Vedas Veda means Knowledge. It is the belief of Hindus that any kind of knowledge, either mundane or divine, can be traced in the Vedas. It is also opined that the Vedas are eternal and deal with the Reality. The Vedic Mantras, or the divine statements, were discovered by the great Rishis during the Samadhi state of their penance. Several Rishis were involved in the discovery of millions of Mantras, which were compiled by the Sage Veda Vyasa and were segregated into four Vedas, viz., Rigveda, Yajurveda, Samaveda and Atharvaveda. The same were further subdivided into 1,131 branches. This information is found in Srimad Bhagavatham of Veda Vyasa, MahaBhashyam of Patanjali and the commentary of Sri Vishnu Sahasra Nama Stotra of Jagadguru Sankaracharya. However, as on date, only 13 Vedic branches could be located, after a search of past 150 years.among these 13 branches, only 7 branches are being studied. The rest of the 6 branches are not having the teachers and students. It means that more than 99% of Vedic literature has disappeared. Even this remaining part of Vedic literature is too extensive to understand, as they deal with, in addition to the main topics of Yajnas and Moksha, the physical sciences, biological sciences, Jyotisha, and Aeoronautics. They also deal with the subjects of Medicine, Structural Engineering etc. To understand the Vedas, it is a prerequisite to acquire the knowledge of Vedangas. Then only the meanings of keywords and other terms of Vedas can be followed. In this context, it may be noted that the Vedas and Vedangas have 3
given prominent place for mathematics. Subsequently several books were written in ancient times about the mathematics in Vedas. Some of the authors of that category are Boudhayana, Garga, Medhatithi, Parasara, Kasyapa, Maya and Brihaspati. The great mathematicians of subsequent times like AryaBhatta, Varahamihira and Bhaskaracharya belong to this category only. From the writings of historians, it is learnt that this subject was taken to Arab countries from this country only. It seems that a Pandit of Ujjain, by name Kanka, was invited to Bagdad by Kharif Al Mansur in 770 A.D. There he he taught the subjects of mathematics and Jyotisha to the Arab scholars. Only with his support, the book titled BrahmaSphuta Siddhanta of Brahmagupta could be translated into Arabic language. M.Nev, the French Scientist stated in his book On new light on our numerals, that the Hindu numerals were in use in Syria in 7 th century A.D. itself. Some important topics that are covered in the present series of books are as follows: Decimal number system Names of numbers of high order, as found in Vedas, Ramayana, Lilavati Ganitham etc. Even numbers and Odd numbers Arithmetical operations - Additions - Subtractions - Multiplications - Divisions - Powers of Numbers 4
Positional notation Vulgar fractions Astronomical calculations Statistics Geometry Set theory It may please be noted that the main objective of the present series is to create awareness among our children about our rich heritage and the contributions of India to Mathematics in ancient times. It is also to create interest among the children on the subject of mathematics and remove fear complex, to the extent possible. References : The world famous book titled Vedic Mathematics of H.H. Sri Bharathi Krishna Tirtha Swamiji is the main source for these booklets.however,several other old books like AryaBhatiyam, Pavuluri Ganitham, Lilavathi Ganitham and ancient scriptures are referred extensively as and where needed. Simultaneously the books of contemporary mathematicians like Sakuntala Devi are also considered for the benefit of the learners. Note : During the process of explanation, certain fundamental topics, which are generally known, are also covered for maintaining the sequence. If it appears as trivial, a reader may skip that portion and proceed to the next section unhesitatingly. Acknowledgements : We are grateful to Dr. K. Ramesh, Scientific Officer, DAE, Nagarjuna Sagar, for his scrutiny of this book. 5