VEDIC MATHEMATICS

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INDEX

Foreword 4

Preface 7

1. Introduction to Vedic Mathematics 9

2. Simple Practice of Numbers 15

3. Digital Roots of Numbers 46

4. Multiplication Tables & Digital Roots 55

5. Additions-Dot Method 61

6. Subtractions-Dot Method 68

7. Multiplications-1 (Ekadhikena Purvena) 76

8. Multiplications 2 (Antyayordasakepi) 83

9. Multiplications 3 (Eka Nyunena Purvena) 89

10. Positinal Notation in Vedas 103

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FOREWORD

INTRODUCTION

The subject of Vedic Mathematics has become a householdname in recent years. In fact it is very ancient and is known inIndia for several thousands of years.The term Vedic mathematicsindicates that mathematics which has its origin in theVedas.Then, what is Veda? Veda means knowledge, whichincludes both the spiritual knowledge and worldly knowledge.

Lagadha, the great mathematician of India of about1500b.c., states in his book of Vedanga Jyotisha that “Like thecrest of a peacock, and like the gems on the hoods of serpants,the mathematics lies at the top of all knowledge systems.”

Our sages in ancient t imes discovered severalmathematical principles in our Vedic literature. Recently, in1960s, Swami Bharati Krishna Tirtha of Govardhan peeth ofPuri Jagannath, authored a book titled Vedic Mathematics.

ADVANTAGES OF LEARNING VEDIC MATHEMATICSBY THE STUDENTS OF MODERN EDUCATION

1. Vedic mathematics helps to eliminate the phobia of manyschool children who consider mathematics as a difficultsubject.

2. Vedic maths is easy to learn, faster to use and less proneto errors.

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3. Highly useful for competitive examinations.

4. Provides one line answers, using mental and super fastmethods.

5. Offers a new approach based on pattern recognition.

6. Develops student’s creativity with a high degree ofmathematical ability,

7. Carries great educational value.

GOLDEN NANDI AWARD FOR VEDIC MATHEMATICS

We are happy to inform that we commenced gatheringthe data related to Vedic mathematics in 1972, and subsequentlypublished series of articles in various journals. Further we gotan opportunity to teach the subject of Vedic mathematics at masslevel in Andhra Pradesh, through Bhakti TV Channel.Incidentally, this program was adjudged as the “First BestEducational TV Programme for the year 2008, and GoldenNandi Award was presented to us by Govt. of Andhra Pradesh.

BOOK SERIES FOR STUDENTS OF VARIOUS CLASSES

With this background,a series of books on Vedicmathematics are prepared by us, for the benefit of students, ofclass 4 to class 8, keeping the average absorption capacity of thestudents in view. The books on Vedic mathematics for otherclasses are also under preparation.

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ACKNOWLEDGEMENTS

It is heartening to note that several Correspondents andHeadmasters, of various High Schools have been expressingtheir strong desire and pressing us to prepare the books forintroducing this subject in their schools. We are grateful to allof them for giving us an opportunity to participate in this missionat high school level on regular basis.

We also acknowledge the support extended by ourstudents Smt. Ganti Rama Devi and Smt. N. Annapurna inpreparing the work sheets for various lessons.

BEST WISHES TO THE STUDENTS

With our experience, we are sure that the students willenjoy the fun of learning this Vedic mathematics and we offerour best wishes to the students in their educational pursuit. Wesincerely invite feedback from the teachers and students, whichwill be highly useful for updating the books in future.

Hyderabad Dr. Remella Avadhanulu11.06.2014 Author

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PREFACEWithout mathematics there is no living and no civilization.

For instance, measuring time guides us through every moment ofour lives even though we are not conscious of it all the while.

There is another significant aspect about mathematics. Theprocess of learning mathematics tunes pupil’s mind to think in alogical and analytical way. Logical and analytical faculties wouldnot only be helpful in one’s own profession but also be useful infacing other challenges as well.

Contrary to the misguided notion, mathematics is the simplestof all sciences, easy to comprehend. With little more effort, teachersof mathematics, particularly at the primary and middle school levelscan dispel this unsubstantiated fear from the minds of children.

It is in this context, I look at the great utility of Vedicmathematics.

Vedic thinkers invented and conceptualized several ideas suchas number system, counting, basic operations such as addition,subtraction, multiplication and division in the simplest possibleways, the solar system, planetary motion etc. Apart from theseoutstanding contributions, our ancestors gave to the mankind anamazing gift, the concept of zero. The quest for taking mathematicalknowledge to great heights continued in post Vedic period as welland continued till 12th century. Varahamihira, Aryabhatta, Bhaskara,Mahavira and others took forward mathematics further and mademonumental contributions in the areas of algebra, calculus,geometry and astronomy.

The long colonial rule on onside and the rapid advance ofsciences in the west on the other pushed our ancient knowledge ofmathematics and other sciences into oblivion. However during 20th

century efforts were made by scholars to reinvent Vedicmathematics. Several articles and books published in recentdecades created zeal among scholars all over the country torediscover the long neglected knowledge.

However one question that has been troubling many Indianscientists is how to integrate the Vedic scientific concepts into the

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modern science so that we can have the benefits of both.Dr. Remella Avadhanulu, himself a nuclear scientist, through hishard work spread over 40 years, satisfactorily found a solution tothis question.

Dr.Avadhanulu, whom I knew for the past four decades, isexceptionally brilliant. Apart from possessing a deep insight intoadvanced mathematics, physics, computer science etc. he is also agreat scholar in Sanskrit. He is also engaged in the tedious task ofcomputerizing Vedas.

Dr.Avadhanulu has translated Vedic mathematical formulaeand theorems embedded in Sanskrit slokas into simple Englishand further explained them with examples. He took popularizationof Vedic Mathematics as a mission and taught through electronicmedia. His lessons in Bhakti TV have attracted a large number offollowing, both teachers and students. He conducted several shortterm courses for teachers. The students who have been preparingfor competitive examinations suchas JEE-IIT found a very usefultool in these fast calculating methods. Some schools have realizedthe effectiveness of Vedic mathematics and started special classes.

Vedic mathematics has now become so sought after that thereis a demand even from blind students! There could be no greatertribute to the work of Dr. Avadhanulu than this. An edition of VedicMathematics in Braille script is on the anvil.

Dr.Avadhanulu, has now reorganized Vedic mathematicsuseful for students studying in 4th to 8th classes. These text books,I believe, would bring in a revolutionary change in mathematicsteaching in days to come.

Dr.Avadhanulu’s work is monumental and would be usefulfor generations to come.

Hyderabad Prof. S.V. Seshagiri Rao16 June 2014 Prof. of Mathematics & Former Head, Dept. of Geophysics

Osmania University

VEDIC MATHEMATICS

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INDEX

Foreword 4

1. Knowing About Numbers 6

2. Numbers in Sanskrit 9

3. Positional Notation in Vedas 10

4. Positional Notation in Lilavati Ganitham 11

5. Positional Notation in Valmiki Ramayana 12

6. Complement - Nikhilam 13

7. Digital Root 16

8. Geometrical Symmetry in Multiplication Tables 21

9. Additions 23

10. Subtractions with Nikhilam 26

11. Multiplications - Nikhilam Method 32

12. Multiplications - Anurupyena 40

13. Multiplications - Eka nyunena Purvena 47

14. Multiplications by 11 51

15. Meru Prastaram 55

16. Multiplications by 12 57

17. Multiplications by 25 60

18. Multiplications by 5 & 50 61

19. Multiplications by 125 62

20. Multiplications - Urdhva Tiryaghbyam 63

WORK SHEETS 71-110

VEDIC MATHEMATICS

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INDEX

Foreword 4

1. Decimals 6

2. Multiplications - Diagonal Method 11

3. Multiplications - with 8 16

4. Multiplications - with 9 18

5. Multiplications - with 15,18 etc., 20

6. Multiplications - 5 techniques 23

7. Divisions by 5; 25 and 125 32

8. Division by 9 34

9. Divisions - Ekadhikena Purvena 40

10. Divisions - Vilokanam Method 50

11. Division by Numbers lower than the base 55

12. Division by Numbers above the Base 10 59

13. Division by Numbers above the base 100 62

14. Infinity 64

15. Divisibility Rules 65

16. Prime and Composite Numbers 69

17. HCF & LCM 72

18. Vinculam - Mishrank 76

WORK SHEETS 81-131

VEDIC MATHEMATICS

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INDEX

Foreword 41. Squares - 11 type 62. Squares - 22 type 83. Squares - 101 type 104. Squares - Yaavadunam 125. Squares - Yaavadadhikam 156. Squares - Summary 177. Finding the Duplex 238. Square of any number by using Duplex formula 269. Squares of Triple digit Numbers 2710. Peculiarities of Some Mathematical operations 2911. Squares - Technique 1 3812. Squares - Technique 2 3913. Squares - Technique 3 4714. Squares - Technique 4 5115. Squares - Technique 5 5416. Square Roots of exact Squares 5717. Square Roots of numbers in decimal form 6018. Square Roots - Technique 1 6219. Square Roots - Technique 2 6420. Square Roots - Technique 3 7521. Square Roots - Technique 4 8122. Square Roots - Technique 5 8923. Averages - Vyasti, Samasti 9724. Percentage 9925. Percentile 10426. Time and Work 10527. Ratio and Proportion 10728. Unitary Method 10929. Profit and Loss 11030. Ancient Mathematicians of India 11431. Contributions of Indian Mathematiciens 116

WORK SHEETS 118-158

VEDIC MATHEMATICS

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INDEX

Foreword 4

1. Cubes - Technique 1 6

2. Cubes - Technique 2 10

3. Cubes - Technique 3 17

4. Cubes - Technique 4 25

5. Cubes - Technique 5 28

6. Cube Roots - Technique 1 30

7. Cube Roots - Technique 2 31

8. Cube Roots - Technique 3 50

9. Cube Roots - Technique 4 55

10. Cube Roots - Technique 5 64

11. Fourth Order Roots 70

12. Fifth Order Roots - 1 71

13. Fifth Order Roots - 2 72

14. Bhuta Samkhya / Samjnaa Nighantu 76

15. Katapayadi System - 2 78

16. Logn Term Calendar 83

17. Introduction of Algebra 93

18. Decimal Number System in Vedas 98

19. List of All Sutras used in the Text with their Applications 105

20. Indian Algebra in Magic Squares 107

21. Magic Squares with Katapayadi Numbers 110

WORK SHEETS 113-139