Vedic MathsSnigdha 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 South-Indian states)

Paper presentation – Kishora Varga

Kopalle Lavanya Snigdha, X, ‘Ga’

Saraswati Sisu Mandir, Kushaiguda, HyderabadSeptember 2014

Vedic Mathematics generates curiosity and develops problem solving abilities in students

I am very thankful for this opportunity

I would like to start with reverent prostrations to

God AlmightyVedic 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

AryabhataBhaskarachrya II Sridharacharya

My grateful salutations to

Shri Bharati Krihna Teertha Swami, Former Sankaracharya, Govardhan Math, Puri, The father of Modern Vedic MathematicsRev.Bharati Krishna Tirtha Swami

And grateful acknowledgements

To my Gurus, Mentors and elders

To my parentsTo the learned JudgesAnd 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 ApproachHowever, in my talk today in a humble way I would like to try to establish the proposition bya)Quoting from learned authorsb)Enumerating the qualities of

Vedic Mathsc) Citing results of earlier surveyAnd 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 EinsteinOnly 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 improved memory.

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 mental agility. And this in turn leads to growth in other subjects.

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

How does Vedic Maths help?

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 styleThe 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 tables and pages and pages of proof

AnkamulaVery 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.

AnkamulaBut, 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.

We do not have such concepts in conventional maths

Squares of NumbersThere 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 NumbersNow 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 digit number

Antyor Dasake ApiThis 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) = 42. so 62 x 68 = 4216

Antyor Dasake ApiNow 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 + aba2 + b2 + 2ab = c2 + 2aba2 + b2 = c2

a b

c

a

b

23

4 1

ab

1

2

4 3

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 = 8419You may be wondering what this means?

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

Dhanyavaadam