A MODERN INTRODUCTION TO ANCIENT INDIAN MATHEMATICS T.S. Bhanu Murthy Publisher: Wiley Eastern Ltd, New Delhi Price : Rs 70

HOW MUCH is 87265 multiplied by 32117? In our familiar method of multiplication, it will take five steps of multiplication and one step of addition to obtain the answer, apart from the rechecking to ensure the answer is correct. Yet, if the relevant formula from Vedic mathematics is known, the answer can be written down straightaway as 2802690005. Even more remarkably, the answer can be written down forwards or backwards, that is, from right to left or left to right.

What is 1/19 when expresssed in decimals? Vedic mathematics tells you several steps of division are not needed to write down the answer: 0.052631578947368421. Do you have to divide 7031985 by 823? By observation, you would know that the quotient is 8544 and the remainder 273. What is the square root of 738915489? While others reach for an electronic calculator, the Vedic maths adept would write down the answer as 27183. All of these are applications of 16 sutras (formulas) of Vedic mathematics, which encompass arithmetical computations, algebra, geometry, conic sections and even calculus.

Jagadguru Shankaracharya Shri Bharati Krishna Tirtha Maharaja's book on Vedic mathematics has been immensely popular and successful. The 16 formulae have diverse applications but a little bit of practice is necessary, because the techniques are completely alien to Western-trained minds. Nevertheless, the investment in time and effort is well worth it and it will pay rich dividends.

The style of Shri Bharathi Krishna Tirtha's book is both popular and inductive, with not all that much of rigorous deductive reasoning. You knew the formulae worked, you accepted this on faith, but you did not necessarily know why the formulae worked and there was no rigorous proof.

T.S. Bhanu Murthy's book provides all this and more. It provides rigorous proof of the propositions in the earlier book and it has a substantial chapter on the Brahmagupta (7th Century) - Bhaskara (1150) equation and another on geometry. The book also explicitly dispels the illusion that there was a stagnation in the development of mathematics in India after the 12th century. The book is not on Vedic mathematics, but on ancient Indian mathematics, of which Vedic mathematics was only a subset.

Bhanu Murthy's book makes more demands on the reader than Jagadguru's volume, which was directed at and is, therefore, comprehensible to the ordinary reader. Bhanu Murthy's book may not be meant for the professional mathematician, but it is for those who have much more than a cursory interest in the subject. Nor is it meant to duplicate the well-known work of B.B. Datta and A.N. Singh.

As the first venture of the Abhinava Vidya Bharati series, the publication is laudable. But a little more care in editing was needed. Is Krishna Tirtha to be spelt as Tirtha (preface), Thirtha (Chapter 2) or Teertha (back cover)? Why should a book on Vedic mathematics have been published in 1978 (p.59)? That was a reprint. The book was first published in Varanasi in 1965.

Chandamshu Chandradhama Kumbhipala.

No, I have not gone mad. These three words give the value of pi as 3.1415926536. How ? Read the book and find out.

*Bibek Debroy is a professor at the Indian Institute of Foreign Trade, New Delhi. *

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