A booklet giving a brief introduction to Vedic Mathematics through a few examples

1. Where Maths is fun
SUCCESS WITH SELF
The Self Development Academy
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e-mail: successwithself@gmail.com

2. Fun With Numbers
Are you afraid of maths? Do you get bored in maths class? Do you feel you are no good at mathematics? Do you feel, though they say maths is logical, we always end up cramming the proofs of theorems, where it says ‘hence proved’ without any logic? If your answers are ‘yes’ to the above questions, you are not alone. It has been estimated by the Basic Skills Agency that around one in five adults have problems understanding basic maths. To do maths you should be good at fast calculations and you think you are not. So, you lose most fun in maths.
If you hate maths there is, in fact, no problem with you or your brain. It is caused, firstly by the way maths is taught in most schools the world over. As maths is a logical subject, it is thought that it should be taught to the left brain. However, a large number of people prefer understanding with their right brain. So, they get put off by the dry reasoning and predominance of strictly defined step-wise procedures. They would like to understand by analogy and patterns.
Second reason for math-phobia is the math-fear. Psychologists have discovered that one of the biggest barriers to understanding mathematics is fear of sums. In the survey by Staffordshire University, Where the participants in the experiment were anxious about the maths, this also affected their abilities in word-based tasks, which they were more confident in.
But, in reality maths can be great fun. And once you get used to the fun of it, you would ask for more. There are different ways to look at maths.
Vedic Mathematics
Vedic Mathematics is a refreshingly new way of looking at old concepts. It looks at patterns emerging in basic arithmetic operations. It uses appropriate techniques to manipulate the numbers taking advantage of the inherent patterns and symmetries. That is why there is no single methodology for all numbers. It has separate techniques for different numbers. Moreover, it relies on the enormous memory power the human brain has and thus most of the vedic mathematics techniques are suitable for carrying out mental arithmetic.
Though the methods are thousands of years old, in fact, probably the oldest of them all, until recently, they have been lying undiscovered in the ancient Indian literature. It was the good fortune of the world that Seer, Philosopher, Great Mathematician and Scientist Jagadguru Swami Sri Bhārati Kŗşņa Tīrthaji Mahāraja unraveled the mysteries of cryptic ‘sutras’ in the Vedas and gave us the invaluable gift of ‘Vedic Mathematics’. Born as Venkataramana Sastry in 1884, obtained Masters Degrees in six subjects and briefly worked in the academic field as lecturer and Principal. He also participated in the freedom struggle. From 1911-1918 Bharati Krishnaji practiced deep meditation and studied metaphysics and Vedas. In his solitude he discerned the “Ganita-Sutras” or easy Mathematical Formulas on which he compiled the monumental work “Vedic Mathematics”. In 1925 he became the Head of the Govardhan Matha Monastery in Puri,Orissa and was the pontiff till 1960 the year of his “Maha Samadhi”. Tirthaji also wrote sixteen volumes, one for each basic sūtra, explaining their applications. Before they were
Yatha sikha mayuranam Naganam manayo yatha Tadvadvedangasastranam Ganitam murdhani sthitam
"Like the crowning crest of a peacock and the shining gem in the cobra‚s hood, mathematics is the supreme Vedanga Sastra

3. published, the manuscripts were lost irretrievably. Swamiji was unperturbed by the loss of manuscripts and indicated that he would rewrite the sixteen volumes. Before falling ill and dying in 1960, Tirthaji was able to rewrite only the first of the sixteen volumes he had composed.
Anka Mula (Digital Root)
Anka Mula is obtained by repeatedly adding the digits in a number until you are left with one digit.
Eg. Find Anka Mula of 58793
5+8+7+9+3 = 32 = 3+2 = 5
so 5 is the Anka Mula of 58793
Nava Sesha Paddhati:
This is a fast method for finding Anka Mula. In the given number drop all nines while adding
Eg. 7893944989
We drop the nines and add the rest of the numbers only
7+8+3+4+4+8 = 34 = 3+4 = 7 Anka Mula of 7893944989 is 7
We can further use this method to make the digits 9 and drop them i.e
7+(2+6)+3+(4+4)+(1+7) = (7+2)+(6+3)+(4+4+1)+7 = 9+9+9+7 is 7 after dropping the nines.
Now find the Anka Mula of the following numbers
A-i) 1873264753 A-ii) 88329917265 A-iii) 986532774992
Why Ganitam (Maths) in Vedas?
A question arises in mind that Vedas being religious books why there is Maths in them?
Ganitam (Maths) was required in ancient India for various rituals. For example, every householder was required to maintain three types of Agnis (fires) in house: Garhapatya, Ahavaneeya and Dakshina.
The Altar (Agnikundam) for each of the fires was of a specific shape
 Garhapatya – Circular
 Avahaneeya – Square
 Dakshina – Semi-circular
But their areas needed to be the same. Such complicated geometric constructions required knowledge of triangles, rectangles and squares, properties of similar figures etc. Sulva Sutras are addendums to Vedas where mathematical computations required for various rituals were enunciated. The root meaning of the word Sulv is to measure, and in due course the word came to mean the rope or cord.
The shape of the Ashwamedhiki Vedika is an isosceles trapezium whose head, foot and altitude are respectively 24√2, 30√2, 36√2 prakramas. Its area is = 36√2 x 1/2*(24√2 + 30√2) = 1944 Sq. Prakramas.
A remarkable approximation to √2 occurs in each of the three Sulvas, Bodhayana, Apasthamba and Katyayana, viz. √2 = 1 + 1/3 + 1/(3*4) - 1/(3*4*34)
This gives √2 = 1.4142156 , whereas the true value is 1.414213.

4. Nikhilam Sutra
Nikhilam Navatah, Charamam Dsatah means all from nine and the last from ten.
Let us do the subtraction 100000 – 75342
Using the Nikhilam Sutra start from the left
9-7 = 2, 9-5= 4, 9-3 = 6, 9-4 = 5, and the last 10-2 = 8 thus 100000 – 75342 = 24658
Thus it becomes a sum which you can do orally without using pen and paper
Let us try one more: 1000000 – 897531 = 102469
Try the following subtractions
i) 1000000 – 283497 ii) 10000 – 4993 iii) 100000000 – 35888997
Astrology & Astronomy required Maths
In ancient India knowledge of Astronomy and astrology were very advanced. The long and arduous computations required therein might have necessitated the invention of methods for fast computations.
Multiplication – Nikhilam sutra
Aadhaara Antara is difference from the base. For multiplying two numbers close to a base number (a power of ten), this method is amazingly simple and fast. The difference from base can be found using sutra ‘Nikhilam Navatah, Charamam Dasataha’ i.e all from nine and last from ten
Consider 97 x 98
Base = 100
difference of base from each number 97 – 100 = -3, 98 – 100 = -2
97 -3 i) write the numbers and differences as shown on left
98 -2 ii) multiply the differences and write as RHS of answer i.e -2 x -3 = 6, but
_____ written as two digits 06, as there are two zeros in the base 100
95 06 iii) Now add -2 to 97 or -3 to 98 to get LHS of answer as 95
_____ iv) The answer is 97 x 98 = 9506
Let’s try one more
9992 x 9988 Let us take Base 10000 and write the numbers and differences as below
9992 -8 i) write the numbers and differences as shown on left
9988 -12 ii) multiply the differences and write as RHS of answer i.e -8 x -12 = 96, but
_________ written as four digits 0096, as there are four zeros in the base 10000
9980 0096 iii) Now add -8 to 9988 or -12 to 9992 to get LHS of answer as 9980
iv) The answer is 9992 x 9988 = 99800096

5. Now try the following
B-i) 989 x 991 B-ii) 9975 x 9993 B-iii) 99999 x 88888 B-iv) 979 x 991
Multiplication by 11
Look at this easy method for multiplying by 11
362718 x 11
03627180 i) put a zero each at either end of the number to be multiplied by 11
________ ii) starting on the right hand side add neighboring two numbers and write in the answer
8 -- iii) 0+8 = 8
9 --- iv) 8+1 = 9
8 ----- v) 7+1 = 8
9 ------ vi) 2+7 = 9
8 -------- vii) 6+2 = 8
9 --------- viii)3+6 = 9
3 ----------- ix) 0+3 = 3
_________
3989898 ---- Answer
_________
Multiply the following numbers by 11
C-i) 2436172609 C-ii) 62718090721 C-iii) 813542713 C-iv)70809011332
Yavadoonam
Square of a number is obtained by multiplying it by itself.
For example square of 12 is 12 x 12 = 144
There is a sutra in vedic mathematics by which we can find squares of numbers close to a base very easily and very fast.
The sutra is ‘yaavadoonam taavadooni kritya varga ca yojayet’ i.e reduce the number by as much as it is less than the base and join its VARGA (Square)
Let us find 9972
Let the base be 1000. Number 997 is 3 less than the base. So subtract the difference 3 from the number i.e 997-3 = 994. This is the LHP of Answer. For the RHP of Answer we have to Square the deficiency i.e. 32=9. But as the base is 1000, the RHP should have 3 digits, so it becomes 009. The final answer is 994009.
And for 1000152
Let the base be 100000. Number 100015 is 15 more than the base. So add 100015+15 = 100030. This is the LHP of Answer. For the RHP of Answer we have to Square the excess i.e. 152=225. But as the base is 100000, the RHP should have 5 digits, so it becomes 00225. So now the final Ans is 10003000225.
Now try
D-i) 99932 D-ii) 99882 D-iii) 100122 D-iv) 100082

6. Inspiration of Vedic Maths
The treasure of Math knowledge in Vedas allowed the Indian mathematicians to discover many great mathematical formulae and principles much before they were (re)discovered by the renaissance mathematicians of Europe.
For example:
Govindaswamin discovered Newton Gauss Interpolation formula about 1800 years before Newton.
Parameswaracharya discovered Lhuiler’s formula about 400 years before Lhuiler.
Nilakanta discovered Newton’s Infinite Geometric Progression convergent series much before Newton.
Bhaskaracharya (5th century) calculated the time taken by the earth to orbit the sun as 365.258756484 days, hundreds of years before the astronomer Smart.
Vegam
Vegam (Veda Ganitam the Amazing Mathematics) is the most fun way of learning maths.
Most teaching in schools is targeted towards left brain learning, while many children are predominantly right brained and would like to learn through analogy and intuition. Vedic maths provides a break from the uniform procedures for all numbers and operations and teaches techniques that take advantage of the inherent patterns and symmetries in numbers to perform large arithmetic calculations amazingly fast. At Vegam children have fun with numbers and learn in play. There are fun games to play and learn. They get instant recognition/reward for doing the class work, and homework. They earn gift slips for active and positive participation, innovative thinking and out of box ideas. They get to watch entertaining, informing and awe-inspiring videos on many mathematical concepts.
Human brain has enormous capabilities and the Vedic Rishis leveraged these to impart whole body of Vedic knowledge exclusively through oral instructions. Many modern inventions have been adversely affecting this unique human endowment. For example electronic calculators reduced the memory capacity of children and their use is now being discouraged in primary schools in the west. In Vegam, emphasis is being placed on carrying out the computations with minimal or no use of paper and pencil, thus sharpening the brain. This will have positive impact not only on Maths learning but other subjects as well.
Several fun games based on Vedic Maths are organized. For example a Vegam Premier League is organized and the teams compete for the VPL Trophy. It is all the fun of Cricket and as a bonus children get to practice Vedic Maths.
Finally it is redeeming our children’s birth right to access their ancestral knowledge, which has taught the world zero and infinity.

7. What will the children learn in Vegam?
The entire mathematics which the child has been learning in school, now appears in a new package. Addition, subtraction, multiplication, Division of long strings of numbers literally appear as child’s play with the new techniques.
In conventional methods, as the lengthy computations are performed by remembering the several steps in the procedure, children tend to make many silly mistakes on the way and end up with wrong results. That erodes their confidence and they develop an aversion and eventually a phobia for Maths.
In Vegam they will learn techniques which are intuitive and simple to remember. Using the techniques they can quickly cross check their answers and become confident about the results.
Levels of Vegam
The course is organized at four levels.
Level 1 - Basic course covers four basic arithmetic operations and Squares.
Level 2 – Advanced course covers advanced multiplication and division techniques, squares and cubes, fractions, Square roots , Cube Roots, LCM and HCF.
Level 3 – Expert Course covering Vedic Algebra and Trigonometry
Level 4 –Master Course covering advanced algebra, trigonometry, coordinate geometry and calculus etc.
Benefits of Vegam
 Children develop confidence in their Math capabilities
 Better scores in Maths Tests and Exams
 With the development of Mental Arithmetic capabilities, can do Maths Tests and Exams quickly and accurately and also get time to cross check again.
 Right Brained children who were hating Maths, appreciate the pattern matching and intuitive methods and thus develop interest in Maths.
 Left Brained children who are already good in Maths will love to use the alternate, fast techniques and score even better in maths.
 With pressure of Math Phobia off their minds children will perform better in all other subjects as well
 Children will love studying maths as it becomes easy and more fun
 Children will develop love and pride for our ancient wisdom and culture and become better citizen.
For Details of the course contact:
SWIS (Success With Self) Learning Academy
Phone: 040 – 27138854, 65552262 e-mail: successwithself@gmail.com

8. Key to the questions
A-i) 1873264753 (1+8)+(7+2)+(1+2+6)+(4+5)+(2+5+2)+1 so Ankamula is 1
A-ii) 88329917265 Ankamula is 6
A-iii) 986532774992 Ankamula = 8
B-i) 989 x 991
989 x 991 Let us take Base 1000 and write the numbers and differences as below
989 -11 i) write the numbers and differences as shown on left
991 - 9 ii) multiply the differences and write as RHS of answer i.e -11 x -9 = 99, but
_________ written as three digits 099, as there are three zeros in the base 1000
980 099 iii) Now add -9 to 989 or -11 to 991 to get LHS of answer as 980
iv) The answer is 989 x 991 = 980099
B-ii) 9975 x 9993 = 99680175
9975 -25
9993 -7
_________
9968 0175
B-iii) 99999 x 88888 = 8888711112
B-iv) 979 x 991 = 970189
C-i) 2436172609
2436172609 x 11
024361726090 i) put a zero each at either end of the number to be multiplied by 11
________ ii) starting on the right hand side add neighboring two numbers and write in the answer
9 iii) 0+9 = 9
9 iv) 9+0 = 9
6 v) 0+6 = 6
8 vi) 6+2 = 8
9 vii) 2+7 = 9
8 viii)7+1 = 8
7 ix) 1+6 = 7
9 x) 6+3 = 9
7 xi) 3+4 = 7
6 xii) 4+2 = 6
2 xiii)2+0 = 2
___________ x) The answer is 26797898699
26797898699

9. C-ii) 62718090721 x 11 = 689898997931
C-iii) 813542713 x 11 = 8948969843
C-iv)70809011332 x 11 = 778899124652
D-i) 99932
Let the base be 10000. Number 9993 is 7 less than the base. So subtract 9993-7 = 9986. This is the LHP of Answer. For the RHP of Answer we have to Square the deficiency i.e. 72=49. But as the base is 10000, the RHP should have 4 digits, so it becomes 0049. The final answer is 99860049.
D-ii) 99882 = 99760144
D-iii) 100122 = 100240144
D-iv) 10008 = 100160064