Most educated Indians know their ancestors contributed to mathematics. Far fewer know the specifics: that Pingala's Meru Prastaar preceded what the West calls Pascal's Triangle by at least 1,800 years; that the binary number system — the foundation of modern computing — was worked out in ancient India; that Baudhayana's Shulbasutra contains what is now taught as Pythagoras' theorem. Chandrahas M. Halai has spent years tracing these contributions back to their primary sources, including original Sanskrit verses, to set the record straight.
Meru Prastaar moves through algebra, progressions, combinatorics, and the mathematics embedded in Pingala's Chandahshastra — showing, step by step, how poetic metre, the binary system, and the famous triangular array all connect to the same body of thought. Later chapters cover modern Indian mathematicians Ramanujan and Kaprekar, showing a tradition that did not end with antiquity. The problems and worked examples throughout make this genuinely accessible rather than merely celebratory.
Secondary school students, competitive exam aspirants, and teachers who want a mathematically honest account of India's contribution to the discipline will find this both a corrective and a foundation.
Table of Contents CHAPTER 1 Why Indian Mathematics? Section I: Algebra Chapter 2 How Many Bees? Chapter 3 Linear Equations with Two Unknowns Chapter 4 Linear Equations with Several Unknowns Chapter 5 Fun with Three-Digit Numbers Chapter 6 Why is Negative Times Negative a Positive? Chapter 7 Arjuna's Arrows and Quadratic Equations Chapter 8 Herd of Elephants and Equations of Higher Degrees Chapter 9 The Broken Bamboo Section II: Progressions Chapter 10 Arithmetic Progression Chapter 11 How Many Spheres? Chapter 12 Aryabhata's Sum of Sums Chapter 13 Story of Invention of Chess and Geometric Progression Chapter 14 Summation of Infinite Geometric Series Section III: Combinatorics Chapter 15 Twenty-four Names of Vishnu and Permutations Chapter 16 Cooking and Combinations Section IV: Pingala's Chhandahshastra Chapter 17 How Pingala Created the Binary Number System Chapter 18 Pingala's Algorithm for Binary Conversion Chapter 19 Prastaar of Kedar Bhatt Chapter 20 Pingala's Algorithm to Find the Value of a Binary Sequence Chapter 21 Quick Exponential Calculation Chapter 22 Meru Prastaar Chapter 23 Pingala's Algorithms for Number of Meters Chapter 24 From Ganas to Octal and Hexadecimal Chapter 25 Narayana Pandit's Sum of Sums of Sums Section V: Miscellaneous Topics Chapter 26 Time, Speed and Distance Chapter 27 A Magic Square for Peace Section VI: Modern Indian Mathematics Chapter 28 Ramanujan's Infinite Nested Radicals Chapter 29 Kaprekar's Constants Chapter 30 From Meru Prastaar to Galton's Board Foreword During the middle of the 7th century CE, a most beautiful Shiva temple known as Kailasha was carved out of a hill of basalt rock at Ellora near Aurangabad in Maharashtra. This temple, the largest monolithic structure in the world, has intricate architecture and superb artwork. Thousands of tonnes of rock were excavated to make this possible. Intricate sculptures were also carved on the ceiling of the temple making the task of the sculptor all the more challenging. One mistake by the shilpi would have ruined the entire project. Kailasha temple is not only an architectural marvel but also an engineering one and proof of the superior engineering skills of the builders. Technological advancement is not possible without the development of mathematics and we have ample evidence that India was the leading scientific and mathematical nation of the ancient world. That ancient India developed the decimal place value number system is widely known, but it is less known that India gave the world the binary number system. Baudhayana's Shulbasutra predates Pythagoras theorem, and both algebra and calculus originated in India. What we popularly call Pascal's triangle is predated by Pingala's Meru Prastara by at least 1800 years, and what is known as the Fibonacci sequence is actually Virahanka's Sankhyanka . People need to be made aware of ancient India's immense contributions to the world of mathematics. This book is a step in this direction. Mathematical creativity in India continued in the medieval era, and modern Indian mathematicians have carried forward this legacy. A glimpse of the contributions in the later phases is also given in the book. Preface Most of the Indians know that their ancestors had made significant contributions to the subject of Mathematics. But very few of us know about what specific contributions were made. People in their pride and / or ignorance make either tall or false claims about ancient Indian Mathematics, thereby doing disservice to our nation and its rich mathematical heritage. There was a need to set the narrative straight and create awareness amongst the masses. As a humble effort in this direction, I started writing and publishing articles and papers on ancient and medieval Indian Mathematics on my blog and other platforms. I have referred to primary or credible sources of information for all my articles and papers on Indian sciences. In most of the places, I have quoted original Sanskrit verses from the texts and then given their meaning in English. Like my articles, I have written this book in interesting and easy to read format so that more people can read and appreciate the contents. Amid overwhelmingly encouraging response to my articles, there were suggestions from many readers that my articles should be compiled into an accessible and informative book on India's mathematical heritage. This motivated me to compile this interesting and introductory book on Indian mathematics written in a popular format. This book not only introduces the reader to Indian mathematics but also clears his / her concepts and builds a strong mathematical foundation. This book also teaches problem solving techniques. This book can be used as a complimentary textbook or as a reference book on higher mathematics by secondary school students as also by their teachers. This book can be a useful resource for students preparing for competitive exams. The book is filled with interesting stories and problems from ancient Indian mathematical texts. The book begins with algebra in section I. This section also makes the reader aware that algebra had originated in India. The section II is on progressions and their sums. There is also a chapter on the summation of infinite geometric series. This chapter makes the reader aware that the summation of infinite geometric series was first done in India. The section III is on combinatorics. The section IV is on the amazing mathematics from Pingala's Chandahshastra . This section also reveals the fascinating connection between poetic meters, combinatorics, binary number system, sums of progressions and the Meru Prastaar. This is the reason why I have named this book Meru Prastaar: The Wonder World of Indian Mathematics . The Section V presents some interesting problems and information from ancient Indian mathematics. The last Section of the book, section VI, gives a glimpse of the work of modern Indian mathematicians Ramanujan and Kaprekar who have carried forward the glorious legacy of Indian mathematics. I would like to advice the reader to read the book in the order it is written. I would also like to advice the reader to go through all the problems given in the book. Ancient and medieval Indian mathematics is a vast ocean of knowledge; this book is just a drop of it. Writing this book has been my humble service to our beloved motherland and its great civilization.
