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Discover Vedic Mathematics

Código del Artículo: NAB932

por Kenneth R Williams

Hardcover (Edición: 2006)

Motilal Banarsidass Publishers
ISBN 8120830962

Tamaño: 9.5 inch X 6.5 inch
Páginas: 216
Weight of the Book: 550 gms

Precio: Euro 22.87

Descripción

Back of the Book

Since the reconstruction of this ancient system interest in Vedic mathematics has been growing rapidly. Its simplicity and coherence are found to be astonishing and we begin to wonder why we bother with out modern methods when such easy and enjoyable methods are available

This book gives a comprehensive introduction to the sixteen formulate on which the system is based showing their application in many areas of elementary maths so that a real feel for the formulae is acquired.

Using simple patterns based on natural mental faculties problems normally requiring many steps of working are shown to be easily solved in one often forwards or backwards.

Vedic Mathematics solutions of examination question are also given and in this edition comparisons with the conventional methods are shown. An account of the significance of the Vedic formulate (Sutras) is also included.

Foreword

Mathematics is universally regarded as the science of all sciences and "the priestess of definiteness and clarity". If, Herbert acknowledges that "everything that the greatest minds of all times have accomplished towards the comprehension of forms by means of concepts is gathered into one great science, Mathematics". In India’s intellectual history and no less in the intellectual history of other civilizations, Mathematics stands forth as that which unites and mediates between Man and Nature, inner and outer world, thought and perception.

Indian Mathematics belongs not only to an hoary antiquity but is a living discipline with a potential for manifold modern applications. It takes its inspiration from the pioneering, though unfinished work of the late Bharati Krishna Tirt aji, a former Shankaracharya of Puri of revered memory who reconstructed a unique system on the basis of ancient Indian tradition of mathematics. British teachers have prepared textbooks of Vedic Mathematics for British Schools. Vedic mathematics is thus a bridge across centuries, civilisations, linguistic barriers and national frontiers.

Vedic mathematics is not only a sophisticated pedagogic and research tool but also an introduction to an ancient civilization. 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, astronomy, 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 traveled 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 new mathematical trails in Cambridge University in the second decade of the twentieth century even though he did not himself possess a university degree.

I do not wish to claim for Vedic Mathematics as we know it today the status of a discipline which has perfect answers to every problem. I do however question those who mindlessly decide the very idea and nomenclature of Vedic mathematics and regard it as an anathema. They are obviously affiliated to ideological prejudice and their ignorance is matched only by their arrogance. Their mindsets were bequeathed to them by Macaulay who knew next to nothing of India’s scientific and cultural heritage. They suffer from an incurable lack of self-esteem coupled with an irrational and obscurantist unwillingness to celebrate the glory of Indian achievements in the disciplines of mathematics, astronomy, architecture, town planning, physics, philosophy, metaphysics, metallurgy, botany and medicine. They are as conceited and dogmatic in rejecting Vedic Mathematics as those, who naively attribute every single invention and discovery in human history to our ancestors of antiquity. Let us reinstate reasons as well as intuition and let us give a fair chance to the valuable insights of the past. Let us use that precious knowledge as a building block. To the detractors of Vedic Mathematics I would like to make a plea for sanity, objectivity and balance. They do not have to abuse or disown the past in order to praise the present.

Preface

This book consists of a series of examples, with explanations, illustrating the scope and versatility of the Vedic mathematical formulae, as applied in various areas of elementary mathematics. Solutions to ‘O’ and ‘A’ level examination questions by Vedic methods are also given at the end of the book.

The system of Vedic Mathematics was rediscovered from Vedic texts earlier this century by Sri Bharati Krsna Tirthaji (184l—196O). Bharati Krsna studied the ancient Indian texts between 191 1 and 19 18 and reconstructed a mathematical system based on sixteen Sutras (formulas) and some sub-sutras. He subsequently wrote sixteen volumes, one on each Sutra, but unfortunately these were all lost. Bharati Krsna intended to rewrite the books, but has left us only one introductory volume written in 1957.This is the book "Vedic Mathematics" published in 1965 by Banaras Hindu University and by Motilal Banarsidass.

The Vedic system presents a new approach to mathematics, offering simple, direct, one-line, mental solutions to mathematical problems. The Sutras on which it is based are given in word form, which renders them applicable in a wide variety of situations. They are easy to remember, easy to understand and a delight to use.

The contrast between the Vedic system and conventional mathematics is striking. Modem methods have just one way of doing, say, division and this is so cumbrous and tedious that the students are now encouraged to use a calculating device. This sort of constraint is just one of the factors responsible for the low esteem in which mathematics is held by many people nowadays.

The Vedic system, on the other hand, does not have just one way of solving a particular problem, there are often many methods to choose from. This element of choice in the Vedic system, and even of innovation, together with the mental approach, brings a new dimension to the study and practice of mathematics. The variety and simplicity of the methods brings fun and amusement, the mental practice leads to amore agile, alert and intelligent mind, and innovation naturally follows.

It may seem strange to some people that mathematics could be based on sixteen word •formulae; but mathematics, more patently than other systems of thought, is constructed by internal laws, natural principles inherent in our consciousness and by whose action more complex edifices are constructed. From the very beginning of life there must be some structure in consciousness enabling the young child to organize its perception learn and evolve. It these principles (see appendix) could be formulated and used they would give us the easiest and most efficient system possible for all our mental enquiries. This system of Vedic Mathematics given to us by Sri Bharati Krsna Tirthaji points towards a new basis for mathematics and a unifying principle by which we can simultaneously extend our understanding of the world and of our self.

This book was first published in 1984 one hundred years since the birth of bharati Krsna. In this edition many new variations have been added as well as many comparisons with the conventional methods so that readers can clearly see the contrast between the two systems. An appendix has been added that describes each of the sixteen sutras as a principle or natural law. In this edition also is a proof of a class of equations coming under the Samuccaya Sutra by Thomas Dahl of Kristianstad University Sweden (see Chapter 10)

Contents

	Foreword	vii
	Preface	ix
	Illustrative Examples	xv
1	All From Nine and the Last From Ten	1
	Subtraction	1
	Multiplication	2
	One Number above and one number below the base	4
	Multiplying Numbers Near Different Bases	4
	Using other bases	5
	Multiplications of three or more numbers	7
	First corollary squaring and cubing of numbers near a base .	9
	Second Corollary Squaring of numbers beginnings or ending in 5 etc	10
	Third Corollary Multiplication by nines	12
	Division	12
	The Vinculum	17
	Simple applications of the Vinculum	18
	Exercise on Chapter 1	20
2	Vertically and crosswise	25
	Multiplication	25
	Number of Zeros after the Decimal Point	28
	Using the Vinculum	28
	Multiplying from left to right	29
	Using the Vinculum	30
	Algebraic Products	31
	Using Pairs of Digits	31
	The Position of the Multiplier	31
	Multiplying a Long Number by a short Number the moving Multiplier Method	32
	Base five Product	33
	Straight Division	33
	Two or More Figures on the Flag	36
	Argumental division	38
	Numerical Application	39
	Squaring	40
	Square Roots	42
	Working two digits at a time	44
	Algebraic Square Roots	44
	Fractions	45
	Algebraci Fractions	47
	Left to Right Calculations	48
	Pythagoras Theorem	48
	Equation of a line	49
	Exercise on Chapter 2	50
3	Proportionately	57
	Multiplication and division	57
	Cubing	58
	Factorising quadratics	58
	Ratios in Triangles	60
	Transformation of Equations	61
	Number Bases	62
	Miscellaneous	63
	Exercises on Chapter 3	64
4	By Addition and by Subtraction	57
	Simultaneous Equations	67
	Divisibility	68
	Miscellaneous	69
	Exercises on Chapter 4	70
5	By Alternate elimination and retention	71
	Highest Common Factor	71
	Algebraic H.C.F	72
	Factorizing	73
	Exercises on Chapter 5	74
6	By Mere Observation	75
	Multiplication	75
	Additional and subtraction from left to right	76
	Miscellaneous	77
	Exercises on Chapter 6	78
7	Using the average	79
	Exercises on Chapter 7	82
8	Transpose and Apply	83
	Division	83
	Algebraic division	83
	Numerical division	86
	The Remainder Theorem	89
	Solution of Equations	90
	Linear Equations in which ‘x’ Appears more than once	91
	Literal Equations	93
	Mergers	93
	Transformation of Equations	94
	Differentiation and integrations	95
	Simultaneous Equations	95
	Partial fractions	96
	Odd and Even Functions	99
	Exercises on Chapter 8	99
9	One Ratio: The Other One Zero	102
	Exercise on Chapter 9	103
10	When the Samuccaya is the Same it is Zero	104
	Samuccaya as a Common Factor	104
	Samuccaya as the Product of the Independent terms	104
	Samuccaya as the sum of the denominators of two fractions having the same	105
	Numerical Numerator	105
	Samuccaya as a Combination or Total	105
	Cubic Equations	108
	Quartic Equations	108
	The Ultimate and twice the Penultimate	109
	Exercise on Chapter 10	109
11	The First by the first and the last by the last	111
	Factorizing	112
12	By the Completion or Non Completion	114
	Exercise on Chapter 12	116
13	By One more than the one Before	118
	Recurring Decimals	118
	Auxiliary Fractions A.F.	121
	Denominators not ending in 1,3,7,9	124
	Groups of Digits	126
	Remainder Patterns	127
	Remainders by the Last Digit .	128
	Divisibility .	129
	Osculating From left to right .	131
	Finding the Remainder	132
	Writing a Number divisible by a given number	132
	Divisor not ending in 9	132
	The Negative Osculator Q	133
	P+Q = D	134
	Divisor not ending in 1,3,7,9.	134
	Groups of Digits	135
	Exercises on Chapter 13.	136
14	The Product of the Sum is the sum of the products	138
15	Only the Last terms	142
	Summation of Series	143
	Limits.	144
	Coordinate Geometry	148
16	Calculus	149
	Integration	153
	Differential Equations	154
	Binomial and Maclaurin Theoremss	155
	‘O’ and ‘A’ Level Examination Papers	157
	‘O’ Level Multiple Choice Paper 1	158
	‘O’ Level Multiple Choice Paper 2	164
	‘A’ Level Multiple Choice Paper 1	168
	‘A’ Level Multiple Choice Paper 2	172
	Answers to Exercise	177
	List of Vedic Sutra	187
	List of Vedic Sub Sutras	188
	Index of the Vedic Sutras	189
	References	191
	Appendix	193
	Index	197