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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 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