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 South-Indian states)

Paper presentation – Kishora Varga

Kopalle Lavanya Snigdha, X, ‘Ga’

Saraswati Sisu Mandir, Kushaiguda, Hyderabad

September 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 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

AryabhataBhaskarachrya II Sridharacharya

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 ApproachHowever, 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

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

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

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.

We do not have such concepts in

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

a2 + b2 = c2a b

c

a

b

23

4 1

a

b

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 = 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