The Power of Vedic Maths with Trigonometry

170 Pages·2005·4.32 MB·English

THE POWER OF
VEDIC
MATHS
2nd EDITION
ATUL GUPTA
Published by Jaico Publishing House A-2 Jash Chambers, 7-A Sir Phirozshah
Mehta Road Fort, Mumbai - 400 001
[email protected]
www.jaicobooks.com
© Atul Gupta
THE POWER OF VEDIC MATHS
ISBN 81-7992-357-6
First Jaico Impression: 2004
Thirteenth Jaico Impression (Revised & Updated): 2010
Fifteenth Jaico Impression: 2011
No part of this book may be reproduced or utilized in any form or by any means,
electronic or mechanical including photocopying, recording or by any
information storage and retrieval system, without permission in writing from the
publishers.
PREFACE
Mathematics is considered to be a dry and boring subject by a large number
of people. Children dislike and fear mathematics for a variety of reasons. This
book is written with the sole purpose of helping school and college students,
teachers, parents, common people and people from non-mathematical areas of
study, to discover the joys of solving mathematical problems by a wonderful set
of techniques called ‘Vedic Maths’.
These techniques are derived from 16 sutras (verses) in the Vedas, which are
thousands of years old and among the earliest literature of ancient Hindus in
India. They are an endless source of knowledge and wisdom, providing practical
knowledge in all spheres of life. Jagadguru Swami Sri Bharati Krshna Tirthaji
(1884-1960) was a brilliant scholar who discovered the 16 sutras in the Vedas
and spent 8 years in their intense study. He has left an invaluable treasure for all
generations to come, consisting of a set of unique and magnificent methods for
solving mathematical problems in areas like arithmetic, algebra, calculus,
trigonometry and co-ordinate geometry. These techniques are very easy to learn
and encapsulate the immense and brilliant mathematical knowledge of ancient
Indians, who had made fundamental contributions to mathematics in the form of
the decimal numerals, zero and infinity.
I have trained thousands of children of all age groups with these techniques
and I find that even young children enjoy learning and using them. The
techniques reduce drastically, the number of steps required to solve problems
and in many cases, after a little practice, many of the problems can be solved
orally. It gives tremendous self-confidence to the students which leads them to
enjoy mathematics instead of fearing and disliking it.
I have written this book in the form of a cookbook, where a reader can grasp
a technique quickly, instead of reading through a large mass of theory before
understanding it. I have considered techniques for major arithmetical operations
like multiplication, division, computation of squares and square roots and
complex fractions, besides a whole lot of other techniques. Each technique has
been explained in detail with the help of solved examples, using a step-by-step
approach and I am sure that the reader will be able to understand and master the
contents easily. Every chapter has a large number of problems for practice and
the book contains over 1000 such problems. The answers are given alongside so
that the reader can either solve the problems orally or use paper and pen and
compare with the given answer. The chapters should be read sequentially to
absorb the material and then can be used for reference in any desired order.
I have also included a special chapter in which I have shown the application
of the techniques to solve problems, collected from several competitive exams.
This is a unique feature of the book and should add to the popularity of the
techniques.
I have tried to make all the examples and answers error-free but if any
mistake is discovered, I will be obliged if I am informed about the same.
Constructive criticism and comments can be sent to me at
[email protected]
ATUL GUPTA
Mobile: [phone]
Contents
Preface
Chapter 1 Two Simple Techniques
Subtraction from 100/1000/10000
Normal Method
Vedic Method
Multiplication with a series of 9s
Multiplication of a number by same number of 9s
Multiplication of a number by greater number of 9s
Multiplication of a number by lesser number of 9s
Chapter 2 Operations with 9
Computation of remainder (Navasesh) on division by 9
Basic method
First enhancement
Second enhancement
Final compact method
Verification of the product of two numbers
Verification of the sum of two numbers
Verification of the difference of two numbers
Verification of the square or cube of two numbers
Limitation in the verification process
Computation of the quotient on division by 9
Method 1
Method 2
Chapter 3 Operations with 11
Multiplication
Divisibility test of numbers by 11
Multiplication with 111
Chapter 4 Multiplication (Nikhilam)
Secondary bases of 50
Secondary base of 250
Secondary base of 500
Secondary bases like 40, 60
Secondary base of 300
Chapter 5 Multiplication (Urdhva Tiryak)
2-Digit multiplication
3-Digit multiplication
Multiplying 3-digit and 2-digit numbers
4-Digit multiplication
Multiplying 4-digit and 3-digit numbers
Chapter 6 Division
Division by a flag of one digit (no remainder)
Division by a flag of one digit (with remainder)
Division with adjustments
Division with a flag of 2 digits
Division with a flag of 3 digits
Chapter 7 Simple Squares
Chapter 8 Square of Any Number
Definition - Dwandwa or Duplex Square of any number
Square of any number
Chapter 9 Square Root of a Number
Chapter 10 Cubes and Cube Roots
Computing cubes of 2-digit numbers
Cube roots of 2-digit numbers
Computing fourth power of 2-digit numbers
Chapter 11 Trigonometry
Triplet
Computing trigonometric ratios
Computing trigonometric ratios of twice the angle
Computing trigonomegtric ratios of half the angle
Chapter 12 Auxiliary Fractions
Divisors ending with ‘9’
Divisors ending with ‘1’
Divisors ending with ‘8’
Divisors ending with ‘7’
Numbers ending with ‘6’
Other divisors
Chapter 13 Mishrank or Vinculum
Conversion to Mishrank
Conversion from Mishrank
Application in addition
Application in subtraction
Application in multiplication
Application in division
Application in squares
Application in cubes
Chapter 14 Simultaneous Equations
Chapter 15 Osculator
Positive osculators
Negative osculators
Chapter 16 Applications of Vedic Maths
Sample problems
Solutions using Vedic maths
Problems for practice
Answers