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Gaurav Tekriwal MATHS SUTRA The Art of Vedic Speed Calculation Contents About the Author Preface 1. Multiplication 2. Addition 3. Subtraction 4. Division 5. Digit Sums 6. Fractions 7. Decimals 8. Recurring Decimals 9. Percentages 10. Divisibility 11. Squares 12. Cubes 13. Square Roots 14. Cube Roots 15. Raising to Fourth and Higher Powers 16. Algebraic Calculations 17. Simultaneous Equations 18. Quadratic Equations 19. Calendars Practice Exercises Acknowledgements Follow Penguin Copyright PENGUIN BOOKS MATHS SUTRA Gaurav Tekriwal is the founder president of the Vedic Maths Forum India. An educator, Gaurav has been imparting high-speed Vedic mental-mathematics skills over the past fifteen years across the globe. He inspires and informs people, helping them to realize their true potential by introducing them to the world’s fastest mental-maths system—Vedic mathematics. Gaurav is the author of Speed Math and his complete DVD set on the topic is popular among students and academicians worldwide. Through television programmes, DVDs, books, workshops and seminars, Gaurav has taken the Vedic maths system to over four million students in India, South Africa, Australia, the United States and Oman. He is a four-time TED speaker, and has been recently awarded the INDIAFRICA Young Visionaries Fellowship by the ministry of external affairs, India. For more information, please visit www.mathssutra.com. To my mother, Madhu Tekriwal, for her unconditional love, support, encouragement and guidance Preface INDIA IS A LAND with a golden heritage. It has given to the world jewels such as yoga (which is now a multibillion-dollar industry), Ayurveda (another multibillion-dollar industry) and chicken tikka (a trillion-dollar taste!). Indians are feted worldwide for their outstanding cricket and maths skills; after all, it was we who discovered Sachin, the zero and the decimal system. This book is about being the Sachin of the decimal system and scoring high in a limited-time competitive examination through the use of maths sutras. Maths sutras are the secret with which ancient Indians performed their feats over 5000 years ago. This system was lost to the world until it was discovered by a scholar in the forests of south India, some fifty years ago; so it can be labelled as a twentieth-century phenomenon. These maths sutras hold the power to speed up your calculations, give you confidence, and make maths fun and interesting. They will help you in studies just the same way the yoga sutras of Patanjali help improve one’s health and the ancient wisdom of Vātsyāna’s Kama Sutra helps one in the field of love. So what are these sutras? Where do they actually come from? Let’s explore that a bit further. We all know that the Indian civilization is one of the oldest in the world. The Indian sages passed on their collected works orally from one generation to the other using codes which unlock various layers of meaning. They compiled four texts in Sanskrit known as the Vedas—meaning‘knowledge’. The Rig Veda, the Yajur Veda and the Sama Veda contain various hymns dedicated to nature gods, whereas the fourth or the Atharva Veda contains a collection of spells, incantations and speculative hymns. It is in these ancient texts that the maths sutras are found in coded form, according to the founder, Tirthaji. Consider this song dedicated to Lord Krishna: Gopi bhagya madhuvrata srngiso dadhi sandhiga khala jivita khatava gala hala rasandara The literal translation is as follows:‘O Lord anointed with the yoghurt of the milkmaids’ worship (Krishna) O saviour of the fallen O master of Shiva / please protect me.’ But when you apply the numerical code and the master key to it you get the value of pi to 32 places of decimal. Unbelievable, isn’t it? Such is the power of the maths sutras, also popularly known as Vedic mathematics. Sutras are original thoughts, spoken or written in a concise and memorable form. Maths sutras are basically short mathematical formulas dealing with arithmetic and algebra. Sixteen of these were rediscovered by Tirthaji. But in this age of technology how relevant are these sutras? With each passing year the scope of these maths sutras gets wider, as globally more and more students deal with maths. This has caused a full-grown numeracy crisis. Here I present some surprising data: 75.2 per cent of all the children in grade five in India can’t do division (three-digits-by-one-digit problems). Source: ASER 2012 by Pratham 73.7 per cent of all children in grade three in India can’t subtract (two-digit problems with borrowing). Source: ASER 2012 by Pratham Almost half of British adult population have the maths skills of an eleven-year-old or less. That’s 17 million adults in the UK alone. Source: Telegraph, UK 46.3 per cent is the maths pass rate in South Africa’s national senior certificate examinations. Maths is a national disaster in the country. Such is the havoc that maths has created across countries. Most children across the world can’t do maths. This is where Vedic maths comes in with its sheer simplicity and comfort, and makes a career possible in the fields of management, engineering, banking, finance and law by helping to crack their respective examinations. The maths sutras open up a world of possibilities for everyone. Problems which once seemed difficult and daunting are child’s play now. The sutras show that, although maths problems may seem abstract and unbelievable in the beginning, they all have principles of logic behind them. Most of the sutras are very visual when you apply them. Take the‘vertically and crosswise’ sutra, for example. The pattern can be extended to do large multiplications and even shortened to do smaller two-digit-by-two-digit sums. This visual pattern makes the sutras very easy to remember and practise. I’ve had a fascinating journey in the field of Vedic mathematics over the last fifteen years. This journey has not only introduced me to some very interesting people but also allowed me to travel the length and breadth of the world— across the seven seas. And wherever I went, right from meeting kids in the slums in Dharavi in Mumbai to the grand casinos of Cape Town in South Africa to Wall Street in New York, I saw there was one thread binding them all—Vedic mathematics.