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Vedic Maths 
Snigdha a student of X class 
in Saraswati Sisumandir , 
Kushaiguda, Hyderabad 
represented her school in 
Vedic Maths Paper 
Presentation. 
She was Runner up at the 
area level (covering all
Vedic Mathematics generates curiosity 
and develops problem solving abilities in 
students 
Paper presentation – Kishora Varga 
Kopalle Lavanya Snigdha, X, ‘Ga’ 
Saraswati Sisu Mandir, Kushaiguda, 
Hyderabad 
September 2014
I am very thankful for this 
opportunity 
I would like to start 
with reverent 
prostrations to 
God Almighty 
Vedic Rishis 
Saunaka, Pingala, 
Boudhayana,etc. 
Kushan Sculpture of Pingala 
Baudhayana
My humble obeisance to 
 Many great 
Mathematicians of 
ancient India - 
Varaha Mihira, 
Aryabhata, 
Bhaskara, etc. 
Varahamihiraa 
Bhaskarachrya II Sridharacharya Aryabhata
My grateful salutations to 
 Shri Bharati Krihna Teertha 
Swami, Former Sankaracharya, 
Govardhan Math, Puri, The 
father of Modern Vedic 
Mathematics 
Rev.Bharati Krishna 
Tirtha Swami
And grateful acknowledgements 
To my Gurus, Mentors 
and elders 
To my parents 
To the learned Judges 
And to you dear 
audience
My Approach 
I am convinced Vedic maths 
creates curiosity and helps 
develop problem solving 
capability 
I believe this is a profound 
subject for study through 
advanced techniques.
My Approach 
However, in my talk today in a humble 
way I would like to try to establish the 
proposition by 
a) Quoting from learned authors 
b) Enumerating the qualities of Vedic 
Maths 
c) Citing results of earlier survey 
And most important of all 
d) citing examples from my own 
learning experience of Vedic Maths
Math is not liked by many people 
everyday I see my friends, 
acquaintances, colleagues, 
and everyone else in my 
grade, and the vast 
majority of them just don't 
like math.
Maths creates aversion and 
hatred 
 Almost one third of Americans would rather 
clean their bathrooms than do a math problem, 
 ‘Change the Equation’ 2010 survey. 
 When Raytheon Corporation asked 1,000 
middle schoolers if they’d rather eat broccoli or 
do a math problem, a majority said broccoli 
 Five out of four people have trouble with 
fractions. 
Steven Wright
Maths is considered an exotic 
subject 
 Since the mathematicians have invaded 
the theory of relativity, I do not 
understand it myself any more. 
Albert Einstein 
 Only professional mathematicians learn 
anything from proofs. Other people learn 
from explanations. 
Ralph Boas
Learning Vedic Maths is Joyful 
activity 
Vedic Mathematics is the 
gift of the Veda to solve the 
problem of mathematics 
anxiety being faced by 
mathematics education in 
the whole world. 
Puri, 1986, p. 8
Vedic Maths is simple and easy 
Sums requiring 30, 50, 
100 or even more … 
cumbrous steps … can 
be answered in a single, 
simple step of work by 
the Vedic method 
Swami Bharati Krishna Tirtha
Vedic Maths is simple and easy 
For example, the answer to 
the problem 1/39 = 0.025641 
may be easily worked on one 
line in less than 10 seconds 
using the Sutra Ekadhikena 
Purvena – One more than the 
previous one 
Puri & Weinless
How does Vedic Maths help? 
 Coherence - Most striking feature of the 
Vedic system is its coherence. Instead of a 
hotchpotch of unrelated techniques the whole 
system is beautifully interrelated and unified: 
 Flexibility- Modern methods have only one 
way of doing a calculation. Vedic Maths 
allows variations. Children enjoy the scope for 
variation and experiment. 
 Improved memory - Vedic Maths 
calculations are easy and can be carried out 
mentally. This mental exercising leads to
How does Vedic Maths help? 
 Promotes creativity - Vedic math encourage 
students to be creative in doing their math. 
Being naturally creative students like to devise 
their own methods of solution. 
 Appeals to everyone - The able child loves 
the choice and freedom to experiment and the 
less able may prefer to stick to the general 
methods but love the simple patterns they can 
use. 
 Increases mental agility - Ultra-easy methods 
of mental calculation leads naturally to develop
How does Vedic Maths help? 
 Efficient and fast - In the Vedic system 
'difficult' problems or huge sums can often be 
solved immediately. 
 Easy, fun - The experience of the joy of 
mathematics is an immediate and natural 
consequence of practicing Vedic 
Mathematics. 
 Methods apply in algebra - Once an 
arithmetic method has been mastered 
the same can be applied to algebraic cases 
of that type
Studies show Vedic Maths is 
enjoyable 
Results from an empirical study 
… indicate that students using 
the Vedic Sutra based approach 
have higher achievement scores, 
… more … skill, and enjoy 
computation more than students 
using conventional methods. 
John M. Muehlman
Vedic Maths is natural human mental 
process 
Mathematics is seen as a human 
process and is therefore 
psychological as well as entirely 
practical. The psychology of 
mathematics involves recognizing 
patterns of thinking when engaged 
in mental processes. 
The sutras also reveal underlying 
spiritual truths which carry a deeper 
meaning.
Vedic Maths is more than mere 
Maths 
The principal driving force for 
developing (Binomial Theorem) 
… was financial gain. However, 
as I pointed out, in India, the 
aesthetics of religious hymnary , 
that sense of Brahma or divine 
order was also a motivating 
drive 
JEHOVAJAH
The Spiritual dimension of Vedic 
Maths 
Modern Mathematics is the 
field of steps, whereas 
Vedic Mathematics is the 
field of pure intelligence 
that gets what it wants 
instantly without steps. 
Maharshi Mahesh Yogi
The Spiritual dimension of Vedic 
Maths 
Yastanna veda kim richa karishyati ya 
it tad vidus ta ime samasate 
Rig Veda 
‘he who does not have self-referral 
consciousness is full of mistakes, he 
who is not established in self-referral 
consciousness does not know how 
to think spontaneously, 
mathematically right 
Maharshi Mahesh Yogi
Sutra style 
The first big difference between conventional and 
Vedic Maths that I noticed is the ‘Sutra’ 
Alpaksharam, Asandigdham, saaravad 
viswatomukham 
Astobhyam, Anavadyam ca sutram sutravido 
viduh 
Of minimal syllabary, unambiguous, pithy, 
comprehensive, continuous and without flaw: 
who knows sutra knows it to be thus 
 Such an efficient aid to memory, so easy to 
memorize, a single sutra has many 
applications. One is spared memorizing long
Ankamula 
Very useful for checking calculations 
and with ‘Nava Sesha Padhdhati 
(Casting off 9s)’ so easy to compute. 
But, in contrast to conventional 
maths, it is not always correct. 
If we make two mistakes which 
compensate each other, Ankamula 
may not find the mistakes.
Ankamula 
But, make two mistakes together, 
which compensate each other - 
such cases occur very rarely in 
practice. 
Though Ankamula may not be 
theoretically acceptable, but it is 
practically very useful. 
We use it in finding divisibility by 3 & 
9, finding square roots etc.
Squares of Numbers 
There is an elegant and very fast 
procedure for finding squares of 
numbers ending in 5 
For example 852 - Right hand part of 
the answer is 5x5=25. 
Left hand part is obtained by the 
sutra ‘Ekadhikena purvena’ 
Ekadhika of 8 is 9. LHS is 8x9=72. 
852 = 7225
Squares of Numbers 
Now the thrilling part is many students 
worked out the solution themselves 
when the teacher asked ‘ How can you 
use it for finding 862. 
We find (85+1)2 using (a+b)2 = 
a2+2ab+b2 We find a2 = 852 using 
above method and add 2ab = 
2x85x1=170 and b2=1x1=1 to it to get 
the answer 862 = 7225+170+1 = 7396. 
 Thus the method can be used for any 2
Antyor Dasake Api 
This sutra is used for multiplying 
numbers whose right hand parts 
add up to 10. 
For example 62 x 68. Right hand 
parts 2+8 = 10 and left hand part 
is same i.e 6. So the sutra can be 
used for multiplication. RHP of 
answer is 2x8 = 16. LHP of 
answer is 6 x 7 (7 is ekadhika of 6)
Antyor Dasake Api 
Now can we use it when LHP are 
not same, for eg. 72 x 68? 
It is very simple 72 x 68 can be 
written as (62+10) x 68 = (62 x 
68) + 10 x 68 = 4216 (by above 
sutra) + 680 = 4896 
This sutra can be used for any 
pair of two digit numbers.
Proof of Bodhayana (Pythogoras) 
theorem – Vedic Method 
 In a right angled triangle if a, b 
are the two sides containing the 
right angle and c is the 
hypotenuse c2 = a2 + b2 
 Side of big brown square = a+b 
 Area of big brown square = area 
of yellow square + area of 
(Triangle 1 + Triangle 3) + area 
of (Triangle 2 + Triangle 4) 
 (a+b)2 = c2 + ab + ab 
 a2 + b2 + 2ab = c2 + 2ab 
b 
1 
2 
4 3 
3 2 
c 
a 
b 
4 1 
a 
 a2 + b2 = c2 a b
I would like to conclude with a small 
riddle 
Please accept my ( 2 – 1) x 
10000+4277 
 2 = 1.4142 (up to 4 decimal 
places) 
( 2 - 1) x 10000 = 4142 
 4142+4277 = 8419 
You may be wondering what this
I would like to conclude with a small 
riddle 
There is a coding system 
called ‘KATAPAYADI’ by 
which alphabets are 
converted to numbers 
According to this coding 
system 8419 can be 
converted to the word
Dhanyavaada 
m

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Vedic mathematics generates curiosity and develops pproblem solving abilities in students 1

  • 1. Vedic Maths Snigdha a student of X class in Saraswati Sisumandir , Kushaiguda, Hyderabad represented her school in Vedic Maths Paper Presentation. She was Runner up at the area level (covering all
  • 2. Vedic Mathematics generates curiosity and develops problem solving abilities in students Paper presentation – Kishora Varga Kopalle Lavanya Snigdha, X, ‘Ga’ Saraswati Sisu Mandir, Kushaiguda, Hyderabad September 2014
  • 3. I am very thankful for this opportunity I would like to start with reverent prostrations to God Almighty Vedic Rishis Saunaka, Pingala, Boudhayana,etc. Kushan Sculpture of Pingala Baudhayana
  • 4. My humble obeisance to  Many great Mathematicians of ancient India - Varaha Mihira, Aryabhata, Bhaskara, etc. Varahamihiraa Bhaskarachrya II Sridharacharya Aryabhata
  • 5. My grateful salutations to  Shri Bharati Krihna Teertha Swami, Former Sankaracharya, Govardhan Math, Puri, The father of Modern Vedic Mathematics Rev.Bharati Krishna Tirtha Swami
  • 6. And grateful acknowledgements To my Gurus, Mentors and elders To my parents To the learned Judges And to you dear audience
  • 7. My Approach I am convinced Vedic maths creates curiosity and helps develop problem solving capability I believe this is a profound subject for study through advanced techniques.
  • 8. My Approach However, in my talk today in a humble way I would like to try to establish the proposition by a) Quoting from learned authors b) Enumerating the qualities of Vedic Maths c) Citing results of earlier survey And most important of all d) citing examples from my own learning experience of Vedic Maths
  • 9. Math is not liked by many people everyday I see my friends, acquaintances, colleagues, and everyone else in my grade, and the vast majority of them just don't like math.
  • 10. Maths creates aversion and hatred  Almost one third of Americans would rather clean their bathrooms than do a math problem,  ‘Change the Equation’ 2010 survey.  When Raytheon Corporation asked 1,000 middle schoolers if they’d rather eat broccoli or do a math problem, a majority said broccoli  Five out of four people have trouble with fractions. Steven Wright
  • 11. Maths is considered an exotic subject  Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more. Albert Einstein  Only professional mathematicians learn anything from proofs. Other people learn from explanations. Ralph Boas
  • 12. Learning Vedic Maths is Joyful activity Vedic Mathematics is the gift of the Veda to solve the problem of mathematics anxiety being faced by mathematics education in the whole world. Puri, 1986, p. 8
  • 13. Vedic Maths is simple and easy Sums requiring 30, 50, 100 or even more … cumbrous steps … can be answered in a single, simple step of work by the Vedic method Swami Bharati Krishna Tirtha
  • 14. Vedic Maths is simple and easy For example, the answer to the problem 1/39 = 0.025641 may be easily worked on one line in less than 10 seconds using the Sutra Ekadhikena Purvena – One more than the previous one Puri & Weinless
  • 15. How does Vedic Maths help?  Coherence - Most striking feature of the Vedic system is its coherence. Instead of a hotchpotch of unrelated techniques the whole system is beautifully interrelated and unified:  Flexibility- Modern methods have only one way of doing a calculation. Vedic Maths allows variations. Children enjoy the scope for variation and experiment.  Improved memory - Vedic Maths calculations are easy and can be carried out mentally. This mental exercising leads to
  • 16. How does Vedic Maths help?  Promotes creativity - Vedic math encourage students to be creative in doing their math. Being naturally creative students like to devise their own methods of solution.  Appeals to everyone - The able child loves the choice and freedom to experiment and the less able may prefer to stick to the general methods but love the simple patterns they can use.  Increases mental agility - Ultra-easy methods of mental calculation leads naturally to develop
  • 17. How does Vedic Maths help?  Efficient and fast - In the Vedic system 'difficult' problems or huge sums can often be solved immediately.  Easy, fun - The experience of the joy of mathematics is an immediate and natural consequence of practicing Vedic Mathematics.  Methods apply in algebra - Once an arithmetic method has been mastered the same can be applied to algebraic cases of that type
  • 18. Studies show Vedic Maths is enjoyable Results from an empirical study … indicate that students using the Vedic Sutra based approach have higher achievement scores, … more … skill, and enjoy computation more than students using conventional methods. John M. Muehlman
  • 19. Vedic Maths is natural human mental process Mathematics is seen as a human process and is therefore psychological as well as entirely practical. The psychology of mathematics involves recognizing patterns of thinking when engaged in mental processes. The sutras also reveal underlying spiritual truths which carry a deeper meaning.
  • 20. Vedic Maths is more than mere Maths The principal driving force for developing (Binomial Theorem) … was financial gain. However, as I pointed out, in India, the aesthetics of religious hymnary , that sense of Brahma or divine order was also a motivating drive JEHOVAJAH
  • 21. The Spiritual dimension of Vedic Maths Modern Mathematics is the field of steps, whereas Vedic Mathematics is the field of pure intelligence that gets what it wants instantly without steps. Maharshi Mahesh Yogi
  • 22. The Spiritual dimension of Vedic Maths Yastanna veda kim richa karishyati ya it tad vidus ta ime samasate Rig Veda ‘he who does not have self-referral consciousness is full of mistakes, he who is not established in self-referral consciousness does not know how to think spontaneously, mathematically right Maharshi Mahesh Yogi
  • 23. Sutra style The first big difference between conventional and Vedic Maths that I noticed is the ‘Sutra’ Alpaksharam, Asandigdham, saaravad viswatomukham Astobhyam, Anavadyam ca sutram sutravido viduh Of minimal syllabary, unambiguous, pithy, comprehensive, continuous and without flaw: who knows sutra knows it to be thus  Such an efficient aid to memory, so easy to memorize, a single sutra has many applications. One is spared memorizing long
  • 24. Ankamula Very useful for checking calculations and with ‘Nava Sesha Padhdhati (Casting off 9s)’ so easy to compute. But, in contrast to conventional maths, it is not always correct. If we make two mistakes which compensate each other, Ankamula may not find the mistakes.
  • 25. Ankamula But, make two mistakes together, which compensate each other - such cases occur very rarely in practice. Though Ankamula may not be theoretically acceptable, but it is practically very useful. We use it in finding divisibility by 3 & 9, finding square roots etc.
  • 26. Squares of Numbers There is an elegant and very fast procedure for finding squares of numbers ending in 5 For example 852 - Right hand part of the answer is 5x5=25. Left hand part is obtained by the sutra ‘Ekadhikena purvena’ Ekadhika of 8 is 9. LHS is 8x9=72. 852 = 7225
  • 27. Squares of Numbers Now the thrilling part is many students worked out the solution themselves when the teacher asked ‘ How can you use it for finding 862. We find (85+1)2 using (a+b)2 = a2+2ab+b2 We find a2 = 852 using above method and add 2ab = 2x85x1=170 and b2=1x1=1 to it to get the answer 862 = 7225+170+1 = 7396.  Thus the method can be used for any 2
  • 28. Antyor Dasake Api This sutra is used for multiplying numbers whose right hand parts add up to 10. For example 62 x 68. Right hand parts 2+8 = 10 and left hand part is same i.e 6. So the sutra can be used for multiplication. RHP of answer is 2x8 = 16. LHP of answer is 6 x 7 (7 is ekadhika of 6)
  • 29. Antyor Dasake Api Now can we use it when LHP are not same, for eg. 72 x 68? It is very simple 72 x 68 can be written as (62+10) x 68 = (62 x 68) + 10 x 68 = 4216 (by above sutra) + 680 = 4896 This sutra can be used for any pair of two digit numbers.
  • 30. Proof of Bodhayana (Pythogoras) theorem – Vedic Method  In a right angled triangle if a, b are the two sides containing the right angle and c is the hypotenuse c2 = a2 + b2  Side of big brown square = a+b  Area of big brown square = area of yellow square + area of (Triangle 1 + Triangle 3) + area of (Triangle 2 + Triangle 4)  (a+b)2 = c2 + ab + ab  a2 + b2 + 2ab = c2 + 2ab b 1 2 4 3 3 2 c a b 4 1 a  a2 + b2 = c2 a b
  • 31. I would like to conclude with a small riddle Please accept my ( 2 – 1) x 10000+4277  2 = 1.4142 (up to 4 decimal places) ( 2 - 1) x 10000 = 4142  4142+4277 = 8419 You may be wondering what this
  • 32. I would like to conclude with a small riddle There is a coding system called ‘KATAPAYADI’ by which alphabets are converted to numbers According to this coding system 8419 can be converted to the word