“Meru Prastaar – The Wonder World of Indian Mathematics” by Chandrahas Halai gives a good feel of the advanced mathematics education in ancient India. The book provides not just a taste of the subject but a complete overview. The difficulty level moves from easy to moderate, with the later chapters meant to be enjoyed by mathematics aficionados. The examples of questions from eons ago also give us a delightful peek into a way of life that used to exist hundreds of years ago. This book will add a new dimension to your children’s education. They will find value in it whether they are little mathematicians or linguists.
A well-researched book, Meru Prastaar gives us a glimpse into the contents of many books in the Indian mathematics tradition, like Lilavati and Bijaganita by Bhaskaracharya, Ganitasarasangraha by Mahavira, Aryabhatiya by Aryabhata, and Ganitakaumidi by Narayana Pandita, to name a few.
Even young children can savour the opening chapters on algebra which begin with a riddle about bees going to the paatali flower, the Kadamba, mango, champaka trees and a bed of lotuses. Notice how, tangentially, the mention of all these flowers native to Bharat builds a close connection with the land. The next problem, also from Lilavati, asks, “From a bunch of lotuses, one-third were offered to Lord Shiva, one-fifth to Lord Vishnu, one-sixth to SuryaDeva and one-fourth to the goddess. The remaining six were offered to the guru. Tell me quickly the number of lotuses in the bunch?” Each of these problems begins with the question in Sanskrit, precisely how it is formulated in the original texts. If we work out these problems with children at home, they will quickly absorb Sanskrit while reading.
The sheer variety of topics used by ancient mathematicians to design practice problems and examples is mind-boggling. We find math problems on romantic themes, jewels, necklaces, animals, trees, gambling, bequeathing property to children, types of chutneys and cooking, palace descriptions, flora and fauna of Bharat. There is more learning here on different topics than meets the eye!
There’s a question about elephants drinking water and another about a lover giving his fiancee some jewels to be made into ornaments. If you think a book on mathematics like Lilavati has to be dry and humorless, you are in for a surprise! Bhaskaracharya peppers it with comments like “Which lady wouldn’t like to have such a fiancé?” He was having fun with mathematics. This sense of fun also comes across in the book Meru Prastaar. As the author Chandrahas Halai says, “Ancient Indian mathematicians had a sense of humor and were fun-loving. They included practical, interesting, and fun-filled samples in their texts to keep students interested in the subject.”
Bhaskaracharya wrote Lilavati to teach his young daughter (also Lilavati) mathematics interestingly. This book was used in Bharat for hundreds of years to teach Mathematics. Learning about square roots through monkeys entering caves and climbing trees – taught this way, which child wouldn’t be interested in square roots?
The chapters move on to more complex algebra from Ganitasarasangraha. There are methods (mentioned with their Sanskrit names) to solve linear equations in two or more unknowns, as mentioned in the famous Bakhshali manuscript. Perhaps your child will ask why this manuscript is presently kept in a library in Oxford.
Chapter 6 deals with Brahmagupta and his rules (called sutras) for doing arithmetic with negative numbers by taking a humorous example of a man who returns home after gambling and tells his wife that he lost five coins. The puzzled wife asks how he can lose five coins when he has only two to begin with. Enter negative numbers!
We then come to quadratic equations, which are explained by taking the example of Arjuna’s arrows! With examples like this, the most math-phobic child will quickly develop an interest in the subject because it is taught through stories, humor, and history. The most focused math genius will learn about geography, history, and other subjects – such a beautiful example of holistic learning. The kind of learning that advanced educators in the West recommend today was already available to us long ago.
In chapter 9, we encounter trigonometry and the sutra in Baudhayana’s Sulbasutra (the Pythagoras theorem). The examples on trigonometry feature colorful anecdotes like a peacock seated on a pole and watching a snake crawling towards its burrow at the bottom of the pole. The child figures out where the peacock caught the snake from the given details.
Section 2 deals with progressions and Aryabhata’s rules. We come to geometric progressions through the story of the invention of chess (or Chaturanga, to use our original word for chess).
Section 3 goes into Combinatorics. Children learn about permutations through the arrangement of ayudhas in the hands of the 24 forms of Bhagavan Vishnu (Chaturvimshati Keshava Nama, which are the names recited at the beginning of Sandhyavandanam).
Section 4 has Pingala’s Chhandahshastra and the fantastic story about the evolution of the binary system of numbers from Sanskrit poetry! The amazing thing is that poetry and mathematics were so interwoven together in Bharatiya education. Many mathematical discoveries of ancient India came from an analysis of Chandas or the poetic meters.
We move on to algorithms for binary conversion and finding the value of a binary sequence. The reader will progress through a series of steps to understand what a prastaar is, and then, of course, it leads us to the book’s title, Meru Prastaar.
Section 5 rounds off the discussion with various other topics like speed, time, and distance, which every modern school child learns. The book ends with a magic square for peace (did you know it is carved as a Chautisa Yantra in the temples of Khajuraho?) The final section is on modern Indian mathematics featuring Ramanujan and Kaprekar, leading up to binomial coefficients, probability, and Galton’s board.
A point of interest is that the author was introduced to Indian mathematics by his grandmother, Lilavati Halai. Oh, the power of a well-chosen name and its ability to influence multiple generations! He says, “Isn’t it amazing that the mathematics developed by Pingala in Chandahshastra at least 2200 years ago can be used not only to understand but also to advance modern mathematics?”
Chandrahas Halai says in his concluding remarks, “This book is a glimpse into India’s great contributions to the world of mathematics. It is now up to today’s youth to carry forward this glorious legacy.” May this book open the door to the wonder world of Indian mathematics for the coming generations!
