Index. Part Part Part Page No.

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2 Index Page No. Part Mathematics in Vedas 3 2. Additions 6 3. Subtractions 9 4. Multiplications Multiplications Complements Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications-9 47 Part Vinculam Numbers Cube Values Cube Values Divisions Symmetry in the Quotient Divisions Divisions Divisions Multiplications Part Decimal number System in Vedas Measures of numbers Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications iv

3 34. Multiplications Multiplications Akshahridayam Positional weightage system Infinity AC and HAL SYMBOLS 157 Part Methodology for Expressing Numbers in Sanskrit Katapayadi System Katapayadi System Katapayadi System in Vedantasastra Katapayadi System in Sangita Sastra Magic Squares with Katapayadi Numbers Magic Squares with katapayadi Numbers Katapayadi System Number of Planetary Revolutions with Katapayadi System Logic Behind the Naming of Weekdaya in Sanskrit Vedic Numerical Codes / Algebraic Notation Matrhematics in Chandas Sastra (Prosody) 210 Part Long term calender Long term calender Long term calender Multiplications - Lilavati Ganitam Method for validation of product of multiplication About Bhaskaracharya Divisions Prime Numbers Reference to numbers like 19,29,39 and 49 in vedas Digits & Numbers -their Characteristics Mystic codes in our Philosophy Digits & Numbers -their Characteristics Divisibility 269 Part Divisions Divisions Divisions Divisions v

4 69. Ancient Mathematicians of India Some Contributions of Indian 289 Mathematicians 71. Squares Squares Squares Squares Squares Square Roots Square Roots Square Roots Square Roots Square Roots Part Cubes Cubes Cubes Cube Roots Cube Roots Cube Roots Cube Roots Cube Roots Fourth Order Roots Fifth Order Roots Fifth Order Roots vi

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6 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

7 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

8 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