Vegam booklet converted word file

Where Maths is fun

SUCCESS WITH SELF The Self Development Academy

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Moula Ali, Hyderabad 500 040. Phone : 040-27138854; 65552262 Mobile : 8978864560

e-mail: [email protected]

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

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.

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


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

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

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.

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: [email protected]

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


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

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

Education

Vegam booklet converted word file