About the Book
In this book the Vedic techniques are applied to ordinary school mathematics for eleven and twelve yearsold. The arithmatic introduced in books 1 & 2 is extended. The book also deals with the initial stages of solving equations, coordinate geometry, approximations, indices, parallels, triangles, ratio and proportion as well as other topics.
Once a basic grounding has been established with the Vedic methods the next stage is the beginning of discrimination. A problem is set and, armed with several techniques, the student must choose the easiest or most relevant for achieving the solution. This book deals with some of the steps required for this training.
About the Author
J.T. GLOVER is head of mathematics at St. James Independent Schools in London where he has been a teacher for eighteen years. He is director of mathematical studies at the School of Economic Science and a Fellow of the Institute of Mathematics and its Applications. He has been researching Vedic mathematics and its use in education for more than twenty years and has run public courses in London on the subject. Other books by the author are: An Introductory Course in Vedic Mathematics, Vedic Mathematics for Schools, Books 1, 2 and Foundation Mathematics, Books 1, 2 and 3.
Preface
Vedic Mathematics for Schools is an exceptional book. It is not only a sophisticated pedagogic tool but also an introduction to an ancient civilisation. It takes us back to many millennia of India's mathematical heritage. Rooted in the ancient Vedic sources which heralded the dawn of human history and illumined by their erudite exegesis, India's intellectual, scientific and aesthetic vitality blossomed and triumphed not only in philosophy, physics, ecology and performing arts but also in geometry, algebra and arithmetic. Indian mathematicians gave the world the numerals now in universal use. The crowning glory of Indian mathematics was the invention of zero and the introduction of decimal notation without which mathematics as a scientific discipline could not have made much headway. It is noteworthy that the ancient Greeks and Romans did not have the decimal notation and, therefore, did not make much progress in the numerical sciences. The Arabs first learnt the decimal notation from Indians and introduced it into Europe. The renowned Arabic scholar, Alberuni or Abu Raihan, who was born in 973 A.D. and travelled to India, testified that the Indian attainments in mathematics were unrivalled and unsurpassed. In keeping with that ingrained tradition of mathematics in India, S. Ramanujan, “the man who knew infinity”, the genius who was one of the greatest mathematicians of our time and the mystic for whom “a mathematical equation had a meaning because it expressed a thought of God”, blazed many new mathematical trails in Cambridge University in the second decide of the twentieth century even though he did not himself possess a university degree.
The real contribution of this book, Vedic Mathematics for Schools, is to demonstrate that Vedic mathematics belongs not only to an hoary antiquity but is any day as modem as the day after tomorrow. What distinguishes it particularly is that it has been fashioned by British teachers for use at St James Independent Schools in London and other British schools and that it takes its inspiration from the pioneering work of the late Bharati Krishna Tirthaji, a former Sankaracharya of Puri, who reconstructed a unique system on the basis of ancient Indian mathematics. The book is thus a bridge across centuries, civilisations, linguistic barriers and national frontiers.
Vedic mathematics was traditionally taught through aphorisms or Sutras. A Sutra is a thread of knowledge, a theorem, a ground norm, a repository of proof. It is formulated as a proposition to encapsulate a rule or a principle. A single Sutra would generally encompass a wide and varied range of particular applications and may be likened to a programmed chip of our computer age. These aphorisms of Vedic mathematics have much in common with aphorisms which are contained in Panini's Ashtadhyayi that grand edifice of Sanskrit grammar. Both Vedic mathematics and Sanskrit grammar are built on the foundations of rigorous logic and on a deep understanding of how the human mind works. The methodology of Vedic mathematics and of Sanskrit grammar help to hone the human intellect and to guide and groom the human mind into modes of logical reasoning.
I hope that Vedic Mathematics for Schools will prove to be an asset of great value as a pioneering exemplar and will be used and adopted by discerning teachers throughout the world. It is also my prayer and hope that the example of St James Independent Schools in teaching Vedic mathematics and Sanskrit may eventually be emulated in every Indian school.
Introduction
This book is intended as the sequel to Vedic Mathematics For Schools Book 2. It assumes at most of the basic methods have been mastered although many are reintroduced or revised.
The methods are based on the system of Vedic mathematical sutras or rules as they are called in the text. There are said to be sixteen of these sutras and about thirteen subsutras. They are to be found in the text of Vedic Mathematics by Sri Bharati Krishna Tirthaji. Due to flexibility in both meaning and application, no distinction is made here between a sutra and a subsutra.
The sutras embody laws, principles or methods of working and do not always easily succumb to rigid classification. Some of them have many applications. Transpose and adjust is one such rule. It applies to solving equations, division in fractions and dividing numbers close to a base. It has many other uses at later stages in mathematics and indicates, not a single or particular algorithm, but a general mental procedure. There are other sutras, such as, When the final digits add up to ten, for which the uses appear to be very limited.
It is because of the many faceted quality of the sutras, and that there are so few of them, mat the subject becomes greatly unified and simplified.
As well as developing further the methods for multiplication and division using All from nine and the last from ten there are also further special methods particularly suited to mental computation. New topics are also introduced. These are equations of straight lines, approximations, parallel lines, compound arithmetic, indices, construction of formulae, brackets, factorisation, decimal conversions, direct and inverse proportion, percentage increase and decrease, pie charts, recurring decimals and the geometry of the octahedron.
The text also contains revision chapters and practice examination papers.
Contents
Chapter 1 
Simple arithmetic 
1 
Chapter 2 
Multiplication by All from 9 and the last from 10 
10 
Chapter 3 
Division 
17 
Chapter 4 
Algebra 
23 
Chapter 5 
Coordinate geometry 
33 
Chapter 6 
Approximations 
42 
Chapter 7 
Practice and revision 1 
46 
Chapter 8 
Geometry 
49 
Chapter 10 
Compound arithmetic 
72 
Chapter 11 
Indices 
81 
Chapter 12 
Further division 
89 
Chapter 13 
Factors and multiples 
95 
Chapter 14 
Triangles 
104 
Chapter 15 
Vulgar fractions: addition and subtraction 
111 
Chapter 16 
Vulgar fractions: multiplication and division 
121 
Chapter 17 
Discrimination in division 
127 
Chapter 18 
Further algebra 
136 
Chapter 19 
Ratio and proportion 
147 
Chapter 20 
Fractions to decimals 
160 
Chapter 21 
The octahedron 
171 
Chapter 22 
Practice and revision 2 
183 

Answers 
197 
About the Book
In this book the Vedic techniques are applied to ordinary school mathematics for eleven and twelve yearsold. The arithmatic introduced in books 1 & 2 is extended. The book also deals with the initial stages of solving equations, coordinate geometry, approximations, indices, parallels, triangles, ratio and proportion as well as other topics.
Once a basic grounding has been established with the Vedic methods the next stage is the beginning of discrimination. A problem is set and, armed with several techniques, the student must choose the easiest or most relevant for achieving the solution. This book deals with some of the steps required for this training.
About the Author
J.T. GLOVER is head of mathematics at St. James Independent Schools in London where he has been a teacher for eighteen years. He is director of mathematical studies at the School of Economic Science and a Fellow of the Institute of Mathematics and its Applications. He has been researching Vedic mathematics and its use in education for more than twenty years and has run public courses in London on the subject. Other books by the author are: An Introductory Course in Vedic Mathematics, Vedic Mathematics for Schools, Books 1, 2 and Foundation Mathematics, Books 1, 2 and 3.
Preface
Vedic Mathematics for Schools is an exceptional book. It is not only a sophisticated pedagogic tool but also an introduction to an ancient civilisation. It takes us back to many millennia of India's mathematical heritage. Rooted in the ancient Vedic sources which heralded the dawn of human history and illumined by their erudite exegesis, India's intellectual, scientific and aesthetic vitality blossomed and triumphed not only in philosophy, physics, ecology and performing arts but also in geometry, algebra and arithmetic. Indian mathematicians gave the world the numerals now in universal use. The crowning glory of Indian mathematics was the invention of zero and the introduction of decimal notation without which mathematics as a scientific discipline could not have made much headway. It is noteworthy that the ancient Greeks and Romans did not have the decimal notation and, therefore, did not make much progress in the numerical sciences. The Arabs first learnt the decimal notation from Indians and introduced it into Europe. The renowned Arabic scholar, Alberuni or Abu Raihan, who was born in 973 A.D. and travelled to India, testified that the Indian attainments in mathematics were unrivalled and unsurpassed. In keeping with that ingrained tradition of mathematics in India, S. Ramanujan, “the man who knew infinity”, the genius who was one of the greatest mathematicians of our time and the mystic for whom “a mathematical equation had a meaning because it expressed a thought of God”, blazed many new mathematical trails in Cambridge University in the second decide of the twentieth century even though he did not himself possess a university degree.
The real contribution of this book, Vedic Mathematics for Schools, is to demonstrate that Vedic mathematics belongs not only to an hoary antiquity but is any day as modem as the day after tomorrow. What distinguishes it particularly is that it has been fashioned by British teachers for use at St James Independent Schools in London and other British schools and that it takes its inspiration from the pioneering work of the late Bharati Krishna Tirthaji, a former Sankaracharya of Puri, who reconstructed a unique system on the basis of ancient Indian mathematics. The book is thus a bridge across centuries, civilisations, linguistic barriers and national frontiers.
Vedic mathematics was traditionally taught through aphorisms or Sutras. A Sutra is a thread of knowledge, a theorem, a ground norm, a repository of proof. It is formulated as a proposition to encapsulate a rule or a principle. A single Sutra would generally encompass a wide and varied range of particular applications and may be likened to a programmed chip of our computer age. These aphorisms of Vedic mathematics have much in common with aphorisms which are contained in Panini's Ashtadhyayi that grand edifice of Sanskrit grammar. Both Vedic mathematics and Sanskrit grammar are built on the foundations of rigorous logic and on a deep understanding of how the human mind works. The methodology of Vedic mathematics and of Sanskrit grammar help to hone the human intellect and to guide and groom the human mind into modes of logical reasoning.
I hope that Vedic Mathematics for Schools will prove to be an asset of great value as a pioneering exemplar and will be used and adopted by discerning teachers throughout the world. It is also my prayer and hope that the example of St James Independent Schools in teaching Vedic mathematics and Sanskrit may eventually be emulated in every Indian school.
Introduction
This book is intended as the sequel to Vedic Mathematics For Schools Book 2. It assumes at most of the basic methods have been mastered although many are reintroduced or revised.
The methods are based on the system of Vedic mathematical sutras or rules as they are called in the text. There are said to be sixteen of these sutras and about thirteen subsutras. They are to be found in the text of Vedic Mathematics by Sri Bharati Krishna Tirthaji. Due to flexibility in both meaning and application, no distinction is made here between a sutra and a subsutra.
The sutras embody laws, principles or methods of working and do not always easily succumb to rigid classification. Some of them have many applications. Transpose and adjust is one such rule. It applies to solving equations, division in fractions and dividing numbers close to a base. It has many other uses at later stages in mathematics and indicates, not a single or particular algorithm, but a general mental procedure. There are other sutras, such as, When the final digits add up to ten, for which the uses appear to be very limited.
It is because of the many faceted quality of the sutras, and that there are so few of them, mat the subject becomes greatly unified and simplified.
As well as developing further the methods for multiplication and division using All from nine and the last from ten there are also further special methods particularly suited to mental computation. New topics are also introduced. These are equations of straight lines, approximations, parallel lines, compound arithmetic, indices, construction of formulae, brackets, factorisation, decimal conversions, direct and inverse proportion, percentage increase and decrease, pie charts, recurring decimals and the geometry of the octahedron.
The text also contains revision chapters and practice examination papers.
Contents
Chapter 1 
Simple arithmetic 
1 
Chapter 2 
Multiplication by All from 9 and the last from 10 
10 
Chapter 3 
Division 
17 
Chapter 4 
Algebra 
23 
Chapter 5 
Coordinate geometry 
33 
Chapter 6 
Approximations 
42 
Chapter 7 
Practice and revision 1 
46 
Chapter 8 
Geometry 
49 
Chapter 10 
Compound arithmetic 
72 
Chapter 11 
Indices 
81 
Chapter 12 
Further division 
89 
Chapter 13 
Factors and multiples 
95 
Chapter 14 
Triangles 
104 
Chapter 15 
Vulgar fractions: addition and subtraction 
111 
Chapter 16 
Vulgar fractions: multiplication and division 
121 
Chapter 17 
Discrimination in division 
127 
Chapter 18 
Further algebra 
136 
Chapter 19 
Ratio and proportion 
147 
Chapter 20 
Fractions to decimals 
160 
Chapter 21 
The octahedron 
171 
Chapter 22 
Practice and revision 2 
183 

Answers 
197 