Contributed by:

This PDF contains :

Abstract,

Keywords,

1. INTRODUCTION,

2. OBJECTIVE,

i) Pertinency of vedic mathematics:

ii) Exemplification of Vedic mathematics:

iii) Leg –up:

iv) The field of vision:

v) Anonymity between vedic mathematics and

integration simplification:

3. CONCLUSION:

Abstract,

Keywords,

1. INTRODUCTION,

2. OBJECTIVE,

i) Pertinency of vedic mathematics:

ii) Exemplification of Vedic mathematics:

iii) Leg –up:

iv) The field of vision:

v) Anonymity between vedic mathematics and

integration simplification:

3. CONCLUSION:

1.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

Vedic Mathematics-India’s Opulent Benefaction

Shikha Singh#1, Akshmeet Kaur#2, Anandita Gautam#3

Research Associate, WISDOM, Banasthali Vidyapith, Rajasthan, India

Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India

Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India

Abstract – Mathematics referred to as the queen of Romans etc. The Vedic system invented the zero,

sciences reflects the “the active will and the reason for Aryabhata was followed by Brahmagupta who

aesthetic perfection”. Logic and mathematics are developed the use of zero, followed by Pythagoras’

commutual. As per the reports, India is facing a huge theorem which was discovered in India and gravity was

Maths Crisis in which 26.1 per cent of children in Class explained in the Rig Veda, 2,400 years before Newton’s

V know division and only 44.1 per cent in Class VIII apple injury. Vedic Mathematics was not known to the

could solve a three digit by one digit division problem. world but with an increase of interest in ancient Sanskrit

In other words, abstract and logical reasoning is their text, the ancient Vedic Mathematics was rediscovered

hurdle. To overcome this, scholars have revived interest by Swami Bharati Krisna Tirthaji (the former

in Vedic Mathematics which was born in the Vedic Age, Shankaracharya of Puri, India) in 1911, he was a great

deciphered towards the beginning of the 20th century, scholar of Sanskrit, Mathematics, History and

by Swami Bharati Krishna Tirthaji. The Sanskrit word Philosophy. His deep study and careful research had

Veda is derived from the root Vid indicating deep deciphered the great mathematical formulas known as

acquaintance. The Sutras apply to almost every branch Sutras that were completely ignored as no one could

of Mathematics making calculations of large numbers relate these to mathematics. Vedic Mathematics (1965)

easier that was nearly impossible in systems like those that is a pioneer work of Bharati Krishna Tirthaji has

of the Greeks, Romans etc. In the vedic system complex techniques of Vedic mathematics. It is considered as a

problem or difficult sum or lengthy equations can often first work towards Vedic Mathematics. In late 1960s a

be solved immediately. It has striking and beautiful copy of his book reached London and from there Vedic

methods which beautifies and systematise mathematics. Mathematics was reborn. The verses are guides to turn

The Vedic system invented the zero, Aryabhata was difficult sums into quick mental math using simple

followed by Brahmagupta who developed the use of rules. The Nikhilam Navatashcaramam Dashatah - 'all

zero, followed by Pythagoras’ theorem which was from nine, last from ten’ – for example, speeds the

discovered in India and gravity was explained in the Rig multiplication of large numbers by breaking them down

Veda, 2,400 years before Newton’s apple injury. The to their common bases: To multiply 48 by 52, the

debate has raised an uncomfortable question for Hindu numbers are broken into (50-2) and (50+2) and the

nationalists on how India lost its mathematical square of the smaller sum (4) subtracted from the square

advantages over the millennia. Thus, our desideratum of the larger (2,500) to reach the answer of 2,496.

lies in highlighting the significance and the vast usage Similarly, division is simplified by multiplying the

of this branch of mathematics. denominator into a base ten number: 44/25 = 176/100 =

1.76. The successors of the Greeks in the history of

Keywords – Vedic Mathematics, Sutras, Vedic system, mathematics were the Hindus. They produced original

concepts and good procedures. They were the first to

Vedas. recognize zero as both a cardinal number and a place

1. INTRODUCTION holder. Bhaskara supplied correct rules for operating

Square one of Vedic mathematics – Isn’t the idea of with irrational numbers. The Hindus created the concept

solving mathematical problems just within the wink of of negative numbers; the earliest known use of negative

an eye fascinating? Veritably, the brownie points here numbers was by Brahmagupta around A.D. 630.

go to Vedic Mathematics inbred in the Vedic Age, Aryabhata went beyond Diophantus in his use of

deciphered towards the beginning of the 20th century, continued fractions to solve indeterminate equations.

by Swami Bharati Krishna Tirthaji. Well, because After Aryabhata and Varahamihira, came Brahmagupta

mathematics, may it be Vedic or modern is not only who was later assessed by Alberuni as the most

about numbers and figures. Many western societies, distinguished mathematician of India. In Brahma-

math is a much dreaded school subject. Vedic math Sphuta-Siddhanta, Brahmagupta has dealt with algebra,

only has 16 rules, each of which is very simple. The arithmetic, geometry and astronomy. Brahmagupta for

Sutras apply to almost every branch of Mathematics the first time dealt with zero and its operations but

making calculations of large numbers easier that was wrongly stated that zero divided by zero is also zero but

nearly impossible in systems like those of the Greeks, is known for arriving at the solution of the

ISSN: 2231-5373 http://www.ijmttjournal.org Page 283

Vedic Mathematics-India’s Opulent Benefaction

Shikha Singh#1, Akshmeet Kaur#2, Anandita Gautam#3

Research Associate, WISDOM, Banasthali Vidyapith, Rajasthan, India

Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India

Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India

Abstract – Mathematics referred to as the queen of Romans etc. The Vedic system invented the zero,

sciences reflects the “the active will and the reason for Aryabhata was followed by Brahmagupta who

aesthetic perfection”. Logic and mathematics are developed the use of zero, followed by Pythagoras’

commutual. As per the reports, India is facing a huge theorem which was discovered in India and gravity was

Maths Crisis in which 26.1 per cent of children in Class explained in the Rig Veda, 2,400 years before Newton’s

V know division and only 44.1 per cent in Class VIII apple injury. Vedic Mathematics was not known to the

could solve a three digit by one digit division problem. world but with an increase of interest in ancient Sanskrit

In other words, abstract and logical reasoning is their text, the ancient Vedic Mathematics was rediscovered

hurdle. To overcome this, scholars have revived interest by Swami Bharati Krisna Tirthaji (the former

in Vedic Mathematics which was born in the Vedic Age, Shankaracharya of Puri, India) in 1911, he was a great

deciphered towards the beginning of the 20th century, scholar of Sanskrit, Mathematics, History and

by Swami Bharati Krishna Tirthaji. The Sanskrit word Philosophy. His deep study and careful research had

Veda is derived from the root Vid indicating deep deciphered the great mathematical formulas known as

acquaintance. The Sutras apply to almost every branch Sutras that were completely ignored as no one could

of Mathematics making calculations of large numbers relate these to mathematics. Vedic Mathematics (1965)

easier that was nearly impossible in systems like those that is a pioneer work of Bharati Krishna Tirthaji has

of the Greeks, Romans etc. In the vedic system complex techniques of Vedic mathematics. It is considered as a

problem or difficult sum or lengthy equations can often first work towards Vedic Mathematics. In late 1960s a

be solved immediately. It has striking and beautiful copy of his book reached London and from there Vedic

methods which beautifies and systematise mathematics. Mathematics was reborn. The verses are guides to turn

The Vedic system invented the zero, Aryabhata was difficult sums into quick mental math using simple

followed by Brahmagupta who developed the use of rules. The Nikhilam Navatashcaramam Dashatah - 'all

zero, followed by Pythagoras’ theorem which was from nine, last from ten’ – for example, speeds the

discovered in India and gravity was explained in the Rig multiplication of large numbers by breaking them down

Veda, 2,400 years before Newton’s apple injury. The to their common bases: To multiply 48 by 52, the

debate has raised an uncomfortable question for Hindu numbers are broken into (50-2) and (50+2) and the

nationalists on how India lost its mathematical square of the smaller sum (4) subtracted from the square

advantages over the millennia. Thus, our desideratum of the larger (2,500) to reach the answer of 2,496.

lies in highlighting the significance and the vast usage Similarly, division is simplified by multiplying the

of this branch of mathematics. denominator into a base ten number: 44/25 = 176/100 =

1.76. The successors of the Greeks in the history of

Keywords – Vedic Mathematics, Sutras, Vedic system, mathematics were the Hindus. They produced original

concepts and good procedures. They were the first to

Vedas. recognize zero as both a cardinal number and a place

1. INTRODUCTION holder. Bhaskara supplied correct rules for operating

Square one of Vedic mathematics – Isn’t the idea of with irrational numbers. The Hindus created the concept

solving mathematical problems just within the wink of of negative numbers; the earliest known use of negative

an eye fascinating? Veritably, the brownie points here numbers was by Brahmagupta around A.D. 630.

go to Vedic Mathematics inbred in the Vedic Age, Aryabhata went beyond Diophantus in his use of

deciphered towards the beginning of the 20th century, continued fractions to solve indeterminate equations.

by Swami Bharati Krishna Tirthaji. Well, because After Aryabhata and Varahamihira, came Brahmagupta

mathematics, may it be Vedic or modern is not only who was later assessed by Alberuni as the most

about numbers and figures. Many western societies, distinguished mathematician of India. In Brahma-

math is a much dreaded school subject. Vedic math Sphuta-Siddhanta, Brahmagupta has dealt with algebra,

only has 16 rules, each of which is very simple. The arithmetic, geometry and astronomy. Brahmagupta for

Sutras apply to almost every branch of Mathematics the first time dealt with zero and its operations but

making calculations of large numbers easier that was wrongly stated that zero divided by zero is also zero but

nearly impossible in systems like those of the Greeks, is known for arriving at the solution of the

ISSN: 2231-5373 http://www.ijmttjournal.org Page 283

2.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

indeterminate equations of second degree in which he between cardinal and ordinal numbers. The word kha,

excelled Aryabhata. He is the first in the world to have which Indian mathematicians used later to denote zero,

used algebra effectively for astronomical calculations. occurs in Vedic only in the senses of hole, opening

His major achievements were in the field of algebra in vacancy or space. The three greatest landmarks in this

which he carried forward the earlier work of Aryabhata. area are the kuttaka, method of Aryabhata for solving

Medatithi, a seer of the Vedic times, is known to have the linear indeterminate equation ay-bx=c, the bhavana

stated very high numerals, e.g. 10 to the power 22 in a law of Brahmagupta, and the cakravala algorithm

systematic way. His name is associated with hundreds of described by Jayadeva and Bhaskara 2 for solving

verses in the Rig-Veda, Atharvaveda and Yajur Veda. quadratic indeterminate equation Dx2+1=y2.

There is however, no evidence available to show that in

Medhatithi’s time, the large numerals were written as 2. OBJECTIVE

they were spoken. The earliest evidence of the use of the

Objective of the study is the essential facts of Vedic

new system has been found in the Bakhshali manuscript,

Mathematics arousing awareness in the young

whose original composition is said to have been made

generation about the importance of Indian culture

around A.D. 200.Later Aryabhata in his Aryabhatiya,

through so that they feel proud to be a part of such a

Varahamihira in his Pancha Siddhanta, Jainbhadra Gani

diversely rich society. This research bring into notice

and others used the place value system of writing

facts about the growing influence of Vedic mathematics

numerals. In no other country was the decimal system of

in various fields in order to simplify complex

place value notation used so early as in India. The

calculations in order to remove the fear of mathematics

system of place value notation of writing numerals is an

in many students by citing examples of the great

Indian contribution to the world of mathematics that is

mathematicians given by India to the world. Thus, study

reckoned as one of the greatest inventions of all times.

aims to brim the rich heritage of India thereby bringing

Aryabhata was one of the most scientific innovators of

to the light the various discoveries done by Indian

ancient India. He is the earliest known Hindus author to

mathematicians and the various claims that India lost in

have worked on algebra. Aryabhata expressed high

the hands of others. Even the students at IITs, St James'

numbers by means of syllables. He indicated a method

School, London, have begun to teach the Vedic system

of arriving at a solution of the indeterminate equations

successfully. Our motive is to throw light on claims like

of the first degree. He is also the first to give a concept

our scientists discovered the Pythagoras theorem but we

of kuttakara or pulveriser which was later developed by

gave its credit to the Greeks. Lastly, we want the

others in India. He also quoted the Pythagorean theorem

students to learn simplified techniques for understanding

in one of his verses. Bhaskara anticipated many of the

math and improve their skills.

discoveries in the field of algebra so that his work could

only be surpassed in the European countries after the

17th and 18th centuries. He was the last of the great i) Pertinency of vedic mathematics:

mathematicians of ancient and medieval India. For the

Vedic Mathematics was taken up as a new alternative

Indians of the Vedic times, the performance of a variety

system of mathematics. British mathematicians got

of sacrifices formed a major part of their religion. These

interested in Vedic mathematics. Many lectures on this

sacrifices were performed at certain precalculated times,

were delivered which later on were collected in the book

and in altars of particular sizes and shapes which led

– Introductory Lectures on Vedic Mathematics. After

their builders to understand and deduce certain practical

the visit of Andrew Nicholas to India between 1981 and

geometrical principles. Construction of these altars was

1987, interest in Vedic maths started to develop in India.

handled by people well versed in it and the art of this is

Vedic mathematics has given a new approach to

contained in scriptures known as sulba sutras.

mathematics. To do calculations quickly, the Indian

Baudhayana Sulba Sutra is the oldest and the biggest of

Institute of Technology students are said to use Vedic

them all. It belongs to Krishna of various altars and

Mathematics, St James’ School, London and many other

deals briefly with their shapes and sizes. He describes

schools have started teaching Vedic maths to their

methods for construction of geometrical figures,

students. In India also it is taught in many schools.

combination and transformation of areas, measurement

Students of economics and MBA find it very useful. A

of volumes of areas, and squaring the circle. By 1800

Delhi-based forum known as International Research

mathematics rested upon two foundations, the number

Foundation for Vedic Mathematics and Indian Heritage

system and Euclidean geometry. The 17th centuries

have been giving lectures on Vedic Mathematics since

were the greatest periods of mathematics. What may be

1999 in most of the schools in Delhi. Without a doubt

called the prehistory of zero was expressed in early

there are many advantages of learning Vedic

Vedic by kha which refers to cavities of various sorts

Mathematics. Students develop problem solving ability

and occurs in the Upanishads in the sense of ―space‖.

and it also leads to the development of creative

The Rig-Veda made use of recursion and distinguished

ISSN: 2231-5373 http://www.ijmttjournal.org Page 284

indeterminate equations of second degree in which he between cardinal and ordinal numbers. The word kha,

excelled Aryabhata. He is the first in the world to have which Indian mathematicians used later to denote zero,

used algebra effectively for astronomical calculations. occurs in Vedic only in the senses of hole, opening

His major achievements were in the field of algebra in vacancy or space. The three greatest landmarks in this

which he carried forward the earlier work of Aryabhata. area are the kuttaka, method of Aryabhata for solving

Medatithi, a seer of the Vedic times, is known to have the linear indeterminate equation ay-bx=c, the bhavana

stated very high numerals, e.g. 10 to the power 22 in a law of Brahmagupta, and the cakravala algorithm

systematic way. His name is associated with hundreds of described by Jayadeva and Bhaskara 2 for solving

verses in the Rig-Veda, Atharvaveda and Yajur Veda. quadratic indeterminate equation Dx2+1=y2.

There is however, no evidence available to show that in

Medhatithi’s time, the large numerals were written as 2. OBJECTIVE

they were spoken. The earliest evidence of the use of the

Objective of the study is the essential facts of Vedic

new system has been found in the Bakhshali manuscript,

Mathematics arousing awareness in the young

whose original composition is said to have been made

generation about the importance of Indian culture

around A.D. 200.Later Aryabhata in his Aryabhatiya,

through so that they feel proud to be a part of such a

Varahamihira in his Pancha Siddhanta, Jainbhadra Gani

diversely rich society. This research bring into notice

and others used the place value system of writing

facts about the growing influence of Vedic mathematics

numerals. In no other country was the decimal system of

in various fields in order to simplify complex

place value notation used so early as in India. The

calculations in order to remove the fear of mathematics

system of place value notation of writing numerals is an

in many students by citing examples of the great

Indian contribution to the world of mathematics that is

mathematicians given by India to the world. Thus, study

reckoned as one of the greatest inventions of all times.

aims to brim the rich heritage of India thereby bringing

Aryabhata was one of the most scientific innovators of

to the light the various discoveries done by Indian

ancient India. He is the earliest known Hindus author to

mathematicians and the various claims that India lost in

have worked on algebra. Aryabhata expressed high

the hands of others. Even the students at IITs, St James'

numbers by means of syllables. He indicated a method

School, London, have begun to teach the Vedic system

of arriving at a solution of the indeterminate equations

successfully. Our motive is to throw light on claims like

of the first degree. He is also the first to give a concept

our scientists discovered the Pythagoras theorem but we

of kuttakara or pulveriser which was later developed by

gave its credit to the Greeks. Lastly, we want the

others in India. He also quoted the Pythagorean theorem

students to learn simplified techniques for understanding

in one of his verses. Bhaskara anticipated many of the

math and improve their skills.

discoveries in the field of algebra so that his work could

only be surpassed in the European countries after the

17th and 18th centuries. He was the last of the great i) Pertinency of vedic mathematics:

mathematicians of ancient and medieval India. For the

Vedic Mathematics was taken up as a new alternative

Indians of the Vedic times, the performance of a variety

system of mathematics. British mathematicians got

of sacrifices formed a major part of their religion. These

interested in Vedic mathematics. Many lectures on this

sacrifices were performed at certain precalculated times,

were delivered which later on were collected in the book

and in altars of particular sizes and shapes which led

– Introductory Lectures on Vedic Mathematics. After

their builders to understand and deduce certain practical

the visit of Andrew Nicholas to India between 1981 and

geometrical principles. Construction of these altars was

1987, interest in Vedic maths started to develop in India.

handled by people well versed in it and the art of this is

Vedic mathematics has given a new approach to

contained in scriptures known as sulba sutras.

mathematics. To do calculations quickly, the Indian

Baudhayana Sulba Sutra is the oldest and the biggest of

Institute of Technology students are said to use Vedic

them all. It belongs to Krishna of various altars and

Mathematics, St James’ School, London and many other

deals briefly with their shapes and sizes. He describes

schools have started teaching Vedic maths to their

methods for construction of geometrical figures,

students. In India also it is taught in many schools.

combination and transformation of areas, measurement

Students of economics and MBA find it very useful. A

of volumes of areas, and squaring the circle. By 1800

Delhi-based forum known as International Research

mathematics rested upon two foundations, the number

Foundation for Vedic Mathematics and Indian Heritage

system and Euclidean geometry. The 17th centuries

have been giving lectures on Vedic Mathematics since

were the greatest periods of mathematics. What may be

1999 in most of the schools in Delhi. Without a doubt

called the prehistory of zero was expressed in early

there are many advantages of learning Vedic

Vedic by kha which refers to cavities of various sorts

Mathematics. Students develop problem solving ability

and occurs in the Upanishads in the sense of ―space‖.

and it also leads to the development of creative

The Rig-Veda made use of recursion and distinguished

ISSN: 2231-5373 http://www.ijmttjournal.org Page 284

3.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

intelligence. Students of Vedic Mathematics can not are multiplied as before. The number on the left is

only do simple calculations of subtraction, addition,

obtained by diagonal cross addition:

multiplication but also very complex calculations such

as algebra, geometry, calculus and trigonometry. Our 105 +05

mind is at work with this mathematics so mental

108 +08

sharpness is associated with it. Vedic math is very

effective and at the same time it is easy to learn. Only 16 113 40

Vedic sutras are used to solve the mathematical

The product is 11340.

problem. Sutras are basically word formulae that

describe normal way of solving mathematical problems. The technique that is useful in all cases is based on the

Instead of learning by repetition, Vedic Mathematics

principle of udhvatiryaka and involves cross

involves logic and understanding the fundamental

concepts. One can do calculations much faster than done multiplication. This was developed in India before 8

by using the conventional method that is taught in

century and is bases on a deep understanding of the

schools. It teaches the students to solve same problem in

different ways. It should indeed be a spirited feeling to place value system of representing numbers.

encourage the system being developed in our own

E.g. 534 with 463

We write down the first number as it is, n reverse the

ii) Exemplification of vedic mathematics: second number;

Perchance, the most striking feature of the Vedic system 534

is its coherence. Instead of a mélange of unrelated

364

techniques the whole system is bewitchingly interrelated

and unified: the general multiplication method, for 1

example, is easily reversed to allow one-line divisions

=12(4*3=12)

and the simple squaring method can be reversed to give

one-line square roots. And these are all easily The first digit of the result is obtained by multiplying the

understood. This unifying quality is hitting the spot vertically overlapping nos 4 and 3.The product is 12; the

making mathematics child’s play and enjoyable. For units digit 2 is written as the units digit of the result and

example: Nikhilam is a special multiplication method 1 is carried over to the second digity.364 is then shifted

which is illustrated as follows: left by a digit. The vertically overlapping numbers are

multiplied and the products added. Any carry from the

Eg: multiply 95 by 98 .note that95 is less than 100 5 previous operation is added to this to obtain the

and 98 is 2 less than 100.let us write the two numbers hundreds digit of the result.

and their deviations from 100 with a line separating the 534

two as follows:

364

95 05

31

98 02

=42(3*3+4*6=33

Note that the deviation has 2 digits. The product of 95

and 98 is obtained by multiplying the numbers to the 33+1=34)

right of the line. Then a cross a cross subtraction is

Thus the overlapping digits 3 and 3 as well as 4 and 6

carried out diagonally, to give 93 which occupies the

are multiplied and the two products are added to give

thousands and hundreds places, 9310 is the required

33.The addition of carry 1 gives 4 as second digit of the

result and as a carry of 3.The process is repeated by

Another e.g. Indicating the nikhilam for numbers

again shifting 364 to the left as shown:

greater than the base; 534

For numbers close to some power of 10 eg: if we want 364

to multiply 105 n 108 the we proceed as follows; 531

To the right of the number we write its difference from =242(5*3+3*6+4*4=49

100 with a positive sign. Now the numbers on the right 49+3=52)

ISSN: 2231-5373 http://www.ijmttjournal.org Page 285

intelligence. Students of Vedic Mathematics can not are multiplied as before. The number on the left is

only do simple calculations of subtraction, addition,

obtained by diagonal cross addition:

multiplication but also very complex calculations such

as algebra, geometry, calculus and trigonometry. Our 105 +05

mind is at work with this mathematics so mental

108 +08

sharpness is associated with it. Vedic math is very

effective and at the same time it is easy to learn. Only 16 113 40

Vedic sutras are used to solve the mathematical

The product is 11340.

problem. Sutras are basically word formulae that

describe normal way of solving mathematical problems. The technique that is useful in all cases is based on the

Instead of learning by repetition, Vedic Mathematics

principle of udhvatiryaka and involves cross

involves logic and understanding the fundamental

concepts. One can do calculations much faster than done multiplication. This was developed in India before 8

by using the conventional method that is taught in

century and is bases on a deep understanding of the

schools. It teaches the students to solve same problem in

different ways. It should indeed be a spirited feeling to place value system of representing numbers.

encourage the system being developed in our own

E.g. 534 with 463

We write down the first number as it is, n reverse the

ii) Exemplification of vedic mathematics: second number;

Perchance, the most striking feature of the Vedic system 534

is its coherence. Instead of a mélange of unrelated

364

techniques the whole system is bewitchingly interrelated

and unified: the general multiplication method, for 1

example, is easily reversed to allow one-line divisions

=12(4*3=12)

and the simple squaring method can be reversed to give

one-line square roots. And these are all easily The first digit of the result is obtained by multiplying the

understood. This unifying quality is hitting the spot vertically overlapping nos 4 and 3.The product is 12; the

making mathematics child’s play and enjoyable. For units digit 2 is written as the units digit of the result and

example: Nikhilam is a special multiplication method 1 is carried over to the second digity.364 is then shifted

which is illustrated as follows: left by a digit. The vertically overlapping numbers are

multiplied and the products added. Any carry from the

Eg: multiply 95 by 98 .note that95 is less than 100 5 previous operation is added to this to obtain the

and 98 is 2 less than 100.let us write the two numbers hundreds digit of the result.

and their deviations from 100 with a line separating the 534

two as follows:

364

95 05

31

98 02

=42(3*3+4*6=33

Note that the deviation has 2 digits. The product of 95

and 98 is obtained by multiplying the numbers to the 33+1=34)

right of the line. Then a cross a cross subtraction is

Thus the overlapping digits 3 and 3 as well as 4 and 6

carried out diagonally, to give 93 which occupies the

are multiplied and the two products are added to give

thousands and hundreds places, 9310 is the required

33.The addition of carry 1 gives 4 as second digit of the

result and as a carry of 3.The process is repeated by

Another e.g. Indicating the nikhilam for numbers

again shifting 364 to the left as shown:

greater than the base; 534

For numbers close to some power of 10 eg: if we want 364

to multiply 105 n 108 the we proceed as follows; 531

To the right of the number we write its difference from =242(5*3+3*6+4*4=49

100 with a positive sign. Now the numbers on the right 49+3=52)

ISSN: 2231-5373 http://www.ijmttjournal.org Page 285

4.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

Thus the overlapping are multiplied and added, we get proof or explanation of a method beforehand is not

49, to which we add the carry over 3.The third digit of essential in the Vedic methodology. The Vedic system

the product is therefore 2 and 5 is carried over to the appears to be effective over all ability ranges: the able

fourth digit. child loves the choice and freedom to experiment and

The number 364 is again shifted left and the same the less able may prefer to stick to the general methods

but loves the simple patterns they can use. Artistic types

operation is repeated as shown:

love the opportunity to invent and have their own unique

534 input, while the analytic types enjoy the challenge and

scope of multiple methods because the Vedic system

364

uses these ultra-easy methods mental calculation is

4531 preferred and leads naturally to develop mental agility.

And this in turn leads to growth in other subjects. In the

Vedic system 'difficult' problems or huge sums can often

(42+5=47) be solved immediately. These striking methods are just a

part of a complete system of mathematics which is far

The addition of the products of overlapping digits gives

more systematic than the modern 'system'. Vedic

42 and to this we add the carry 5 to give 7 as the fourth

Mathematics manifests the coherent and unified

digit of the result, and as 4 as the carry. Again, 364 is

structure naturally inherent in mathematics and the

shifted to the and repeat the operation.

methods are direct. Vedic mathematics, a set of

534

supposedly ancient techniques that help even the most

364 numerically challenged to conquer difficult sums, is

surging in popularity as government ministers claim that

4531

they could hold the key to better education

As only 5 and 4 are vertically overlapping their product iv) The field of vision:

yields 20.The carry 4 is added to give 24.The fifth digit

The debate has raised an uncomfortable question for

of the result is thus 4,and 2 will be carried over to the

Hindu nationalists on how India lost its scientific and

sixth digit. Once again shifting 364 to the left by a digit

mathematical advantages over the following millennia.

results in no overlap and therefore the sixth digit of the

Dina Nath Batra said ―Muslim invasions and British

result is only the carry 2.thus 534*463=247242.In

colonial rule were to blame. The ancient knowledge had

modern teaching we usually have one way of doing a

been neglected because we’ve been slaves of the

Mohammedans and the British for 2,000 years. Nalanda

and other places of wisdom were destroyed‖, he said. St

iii) Leg –up: James' School, London, and other schools began to

teach the Vedic system, with notable success. Today this

The Vedic system has many special methods, when a

remarkable system is taught in many schools and

calculation has some special characteristic that can be

institutes in India and abroad, and even to MBA and

used to find the answer more easily. This flexibility adds

economics students. When in 1988, Maharishi Mahesh

to the fun and gives pupils the freedom to choose their

Yogi brought to light the marvels of Vedic

own approach. This in turn leads to the development of

math; Maharishi Schools around the world incorporated

creativity and intuition. The Vedic system does not

it in their syllabi. At the school in Skelmersdale,

insist on a purely analytic approach as many modern

Lancashire, UK, a full course called "The Cosmic

teaching methods do. This makes a vast difference to the

Computer" was written and tested on 11 to 14 year old

attitude which students have towards mathematics. The

pupils, and later published in 1998. According to

ease and simplicity of Vedic Mathematics means that

Mahesh Yogi, "The sutras of Vedic Mathematics are the

calculations can be carried out mentally. A flexible,

software for the cosmic computer that runs this

mental system has leg up over the unpliable ones. Pupils

universe."The difference created by Vedic mathematics

can invent their own methods and are not limited to the

is that it had developed the system of tens, hundreds,

one 'correct' method. This leads to more creative,

thousands, etc., and the basis of carrying the remainder

interested and intelligent pupils. It also leads to

of one column of numbers over to the next. This made

improved memory and greater mental agility. All these

for smooth sailing calculations of large numbers that

features of Vedic math encourage students to be creative

was nearly impossible in other systems, as found with

in doing their math. Being naturally creative students

the Greeks, Romans, Egyptians and even Chinese. The

like to devise their own methods of solution. The Vedic

rising popularity of Vedic maths is partly because of a

system seeks to cultivate intuition, having a conscious

renewed campaign by the nationalist Prime Minister,

ISSN: 2231-5373 http://www.ijmttjournal.org Page 286

Thus the overlapping are multiplied and added, we get proof or explanation of a method beforehand is not

49, to which we add the carry over 3.The third digit of essential in the Vedic methodology. The Vedic system

the product is therefore 2 and 5 is carried over to the appears to be effective over all ability ranges: the able

fourth digit. child loves the choice and freedom to experiment and

The number 364 is again shifted left and the same the less able may prefer to stick to the general methods

but loves the simple patterns they can use. Artistic types

operation is repeated as shown:

love the opportunity to invent and have their own unique

534 input, while the analytic types enjoy the challenge and

scope of multiple methods because the Vedic system

364

uses these ultra-easy methods mental calculation is

4531 preferred and leads naturally to develop mental agility.

And this in turn leads to growth in other subjects. In the

Vedic system 'difficult' problems or huge sums can often

(42+5=47) be solved immediately. These striking methods are just a

part of a complete system of mathematics which is far

The addition of the products of overlapping digits gives

more systematic than the modern 'system'. Vedic

42 and to this we add the carry 5 to give 7 as the fourth

Mathematics manifests the coherent and unified

digit of the result, and as 4 as the carry. Again, 364 is

structure naturally inherent in mathematics and the

shifted to the and repeat the operation.

methods are direct. Vedic mathematics, a set of

534

supposedly ancient techniques that help even the most

364 numerically challenged to conquer difficult sums, is

surging in popularity as government ministers claim that

4531

they could hold the key to better education

As only 5 and 4 are vertically overlapping their product iv) The field of vision:

yields 20.The carry 4 is added to give 24.The fifth digit

The debate has raised an uncomfortable question for

of the result is thus 4,and 2 will be carried over to the

Hindu nationalists on how India lost its scientific and

sixth digit. Once again shifting 364 to the left by a digit

mathematical advantages over the following millennia.

results in no overlap and therefore the sixth digit of the

Dina Nath Batra said ―Muslim invasions and British

result is only the carry 2.thus 534*463=247242.In

colonial rule were to blame. The ancient knowledge had

modern teaching we usually have one way of doing a

been neglected because we’ve been slaves of the

Mohammedans and the British for 2,000 years. Nalanda

and other places of wisdom were destroyed‖, he said. St

iii) Leg –up: James' School, London, and other schools began to

teach the Vedic system, with notable success. Today this

The Vedic system has many special methods, when a

remarkable system is taught in many schools and

calculation has some special characteristic that can be

institutes in India and abroad, and even to MBA and

used to find the answer more easily. This flexibility adds

economics students. When in 1988, Maharishi Mahesh

to the fun and gives pupils the freedom to choose their

Yogi brought to light the marvels of Vedic

own approach. This in turn leads to the development of

math; Maharishi Schools around the world incorporated

creativity and intuition. The Vedic system does not

it in their syllabi. At the school in Skelmersdale,

insist on a purely analytic approach as many modern

Lancashire, UK, a full course called "The Cosmic

teaching methods do. This makes a vast difference to the

Computer" was written and tested on 11 to 14 year old

attitude which students have towards mathematics. The

pupils, and later published in 1998. According to

ease and simplicity of Vedic Mathematics means that

Mahesh Yogi, "The sutras of Vedic Mathematics are the

calculations can be carried out mentally. A flexible,

software for the cosmic computer that runs this

mental system has leg up over the unpliable ones. Pupils

universe."The difference created by Vedic mathematics

can invent their own methods and are not limited to the

is that it had developed the system of tens, hundreds,

one 'correct' method. This leads to more creative,

thousands, etc., and the basis of carrying the remainder

interested and intelligent pupils. It also leads to

of one column of numbers over to the next. This made

improved memory and greater mental agility. All these

for smooth sailing calculations of large numbers that

features of Vedic math encourage students to be creative

was nearly impossible in other systems, as found with

in doing their math. Being naturally creative students

the Greeks, Romans, Egyptians and even Chinese. The

like to devise their own methods of solution. The Vedic

rising popularity of Vedic maths is partly because of a

system seeks to cultivate intuition, having a conscious

renewed campaign by the nationalist Prime Minister,

ISSN: 2231-5373 http://www.ijmttjournal.org Page 286

5.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

Narendra Modi, to lay India’s claim to the cornerstones beauty-a beauty cold and austere, like that of sculpture.

of human knowledge. He marked India’s successful In our legwork, we have tried to bring into account the

mission to Mars last year by claiming its ancient Vedic antiquity of mathematics and then of Vedic mathematics

scientists had conceived of air travel thousands of years in an effort to create awareness about the rich culture of

before the Wright Brothers made their first flight. Not which we should be proud as Indians so that the Golden

only is this, the techniques of Vedic mathematics used in Bird is able to witness many more Aryabhatas and

the processors used in electronic devices. As proposed Bhaskaras in the upcoming years. With a presentation of

by the IEEE, we know that the ever increasing demand the various views on the topic, we have reached to the

in enhancing the ability of processors to handle the conclusion that the methods of Vedic mathematics are

complex and challenging processes has resulted in the quite simple and easy to understand but the views of

integration of a number of processor cores into one chip. various authors regarding the fact that there is no solid

Still the load on the processor is not less in generic evidence to prove that these actually form a part of the

system. This load is reduced by supplementing the main Vedas. But, certainly, this method has gained popularity

processor with Co-Processors, which are designed to not only in solving high school mathematics problems

work upon specific type of functions like numeric but has emerged immense growth leading to the

computation, Signal Processing, Graphics etc. The speed formation of actual multipliers and various other real life

of ALU depends greatly on the multiplier Vedic applications. Along with the above mentions pros and

Mathematics as by employing these techniques in the cons of the topic, we have tried to describe the

computation algorithms of the coprocessor will reduce simplicity of Vedic mathematics to the fullest by

the complexity, execution time, area, power etc. highlighting the closeness of Vedic mathematics with

the theory of Integration Simplification. The two are

v) Anonymity between vedic mathematics and similar in the aspect of saving precious resources like

time and reducing complexity to make things more

integration simplification:

efficient. Vedic Mathematics is a branch of

One fresh thought, one new thought can change your life mathematics; nevertheless the applications of the two in

forever. Perception, simplicity and evaluation have led their respective fields and the motives behind them are

to the spurting out of a methodology that has its roots in similar thereby leading to the involvement of the

the blend of pragmatism and idealism thereby refraining efficient and wise utilisation of resources and

from complexity. The process of Integration exhilaration of more efficacious techniques in the

simplification, in the light construction of reality, is respective areas for their upliftment. Thus, by bringing

based on the psychological concept of differentiation, to the brim, all the necessary facts regarding our topic

assimilation, integration and accommodation. ,we wrap us as proud Indians of a diverse Indian society

Disintegration refers to the misapplication of resources and hope that India gets the acknowledgements of the

like time. Integration refers to harmonizing towards a future discoveries and we are able to witness much

common purpose. It is a pragmatic approach of solving a more inventiveness down the line.

problem or preventing a problem in an interactive

manner .Complexity means distracted effort whereas

REFERENCES:

simplicity is a focused effort. Well, generalizing the

concept of integration simplification, we thereby present [1] Dani, S. G. (2001). Vedic Maths’: facts and myths. One India

One People, 4(6).

a brusque collation between the technique of integration [2] Glover, J. T. (2001). Vedic mathematics for schools. Motilal

simplification and our topic of VEDIC Banarsidass Publication.

MATHEMATICS in terms of simplicity and effective [3] K.S. Shukla, Mathematics — the Deceptive Title of Swamiji’s

utilization of paramount resources like time. Just as the Book, in Issues in Vedic Mathematics, (Ed: H.C.Khare),

theory of integration simplification aims at providing the Rashtriya Veda Vidya Prakashan and Motilal Banarasidass.

[4] K.S. Shukla, Vedic mathematics — the illusive title of Swamiji’s

breaking up of complex problems into simple parts, in book, Mathematical Education, Vol 5: No. 3, January–March

the same way the topic of Vedic mathematics also 1989.

provides alternative ways of easy mathematical [5] Kandasamy, W. V., & Smarandache, F. (2006). Vedic

Mathematics,'Vedic'or'Mathematics': A Fuzzy & Neutrosophic

calculations which involve the use of common sense, an

Analysis: A Fuzzy and Neutrosophic Analysis. Infinite Study.

underlying principle of the above technique which saves [6] Kumar, A. (2008). Vedic Mathematics Sutra. Upkar Prakashan.

a lot of time and energy. [7] Kumar, A., & Raman, A. (2010, February). Low power ALU

design by ancient mathematics. In Computer and Automation

Engineering (ICCAE), 2010 The 2nd International Conference

3. CONCLUSION: on (Vol. 5, pp. 862-865).

[8] Plofker, K. (2009). Mathematics in India (No. Sirsi)

The essence of mathematics is not to make simple things i9780691120676. Princeton: Princeton University Press.

complicated but to make complicated things simple. [9] R. K. Thakur (1 November 2009). Vedic Mathematics. Unicorn

Mathematics possesses not only truth but supreme and Dragon Books. ISBN 978-81-7806-177-1.

ISSN: 2231-5373 http://www.ijmttjournal.org Page 287

Narendra Modi, to lay India’s claim to the cornerstones beauty-a beauty cold and austere, like that of sculpture.

of human knowledge. He marked India’s successful In our legwork, we have tried to bring into account the

mission to Mars last year by claiming its ancient Vedic antiquity of mathematics and then of Vedic mathematics

scientists had conceived of air travel thousands of years in an effort to create awareness about the rich culture of

before the Wright Brothers made their first flight. Not which we should be proud as Indians so that the Golden

only is this, the techniques of Vedic mathematics used in Bird is able to witness many more Aryabhatas and

the processors used in electronic devices. As proposed Bhaskaras in the upcoming years. With a presentation of

by the IEEE, we know that the ever increasing demand the various views on the topic, we have reached to the

in enhancing the ability of processors to handle the conclusion that the methods of Vedic mathematics are

complex and challenging processes has resulted in the quite simple and easy to understand but the views of

integration of a number of processor cores into one chip. various authors regarding the fact that there is no solid

Still the load on the processor is not less in generic evidence to prove that these actually form a part of the

system. This load is reduced by supplementing the main Vedas. But, certainly, this method has gained popularity

processor with Co-Processors, which are designed to not only in solving high school mathematics problems

work upon specific type of functions like numeric but has emerged immense growth leading to the

computation, Signal Processing, Graphics etc. The speed formation of actual multipliers and various other real life

of ALU depends greatly on the multiplier Vedic applications. Along with the above mentions pros and

Mathematics as by employing these techniques in the cons of the topic, we have tried to describe the

computation algorithms of the coprocessor will reduce simplicity of Vedic mathematics to the fullest by

the complexity, execution time, area, power etc. highlighting the closeness of Vedic mathematics with

the theory of Integration Simplification. The two are

v) Anonymity between vedic mathematics and similar in the aspect of saving precious resources like

time and reducing complexity to make things more

integration simplification:

efficient. Vedic Mathematics is a branch of

One fresh thought, one new thought can change your life mathematics; nevertheless the applications of the two in

forever. Perception, simplicity and evaluation have led their respective fields and the motives behind them are

to the spurting out of a methodology that has its roots in similar thereby leading to the involvement of the

the blend of pragmatism and idealism thereby refraining efficient and wise utilisation of resources and

from complexity. The process of Integration exhilaration of more efficacious techniques in the

simplification, in the light construction of reality, is respective areas for their upliftment. Thus, by bringing

based on the psychological concept of differentiation, to the brim, all the necessary facts regarding our topic

assimilation, integration and accommodation. ,we wrap us as proud Indians of a diverse Indian society

Disintegration refers to the misapplication of resources and hope that India gets the acknowledgements of the

like time. Integration refers to harmonizing towards a future discoveries and we are able to witness much

common purpose. It is a pragmatic approach of solving a more inventiveness down the line.

problem or preventing a problem in an interactive

manner .Complexity means distracted effort whereas

REFERENCES:

simplicity is a focused effort. Well, generalizing the

concept of integration simplification, we thereby present [1] Dani, S. G. (2001). Vedic Maths’: facts and myths. One India

One People, 4(6).

a brusque collation between the technique of integration [2] Glover, J. T. (2001). Vedic mathematics for schools. Motilal

simplification and our topic of VEDIC Banarsidass Publication.

MATHEMATICS in terms of simplicity and effective [3] K.S. Shukla, Mathematics — the Deceptive Title of Swamiji’s

utilization of paramount resources like time. Just as the Book, in Issues in Vedic Mathematics, (Ed: H.C.Khare),

theory of integration simplification aims at providing the Rashtriya Veda Vidya Prakashan and Motilal Banarasidass.

[4] K.S. Shukla, Vedic mathematics — the illusive title of Swamiji’s

breaking up of complex problems into simple parts, in book, Mathematical Education, Vol 5: No. 3, January–March

the same way the topic of Vedic mathematics also 1989.

provides alternative ways of easy mathematical [5] Kandasamy, W. V., & Smarandache, F. (2006). Vedic

Mathematics,'Vedic'or'Mathematics': A Fuzzy & Neutrosophic

calculations which involve the use of common sense, an

Analysis: A Fuzzy and Neutrosophic Analysis. Infinite Study.

underlying principle of the above technique which saves [6] Kumar, A. (2008). Vedic Mathematics Sutra. Upkar Prakashan.

a lot of time and energy. [7] Kumar, A., & Raman, A. (2010, February). Low power ALU

design by ancient mathematics. In Computer and Automation

Engineering (ICCAE), 2010 The 2nd International Conference

3. CONCLUSION: on (Vol. 5, pp. 862-865).

[8] Plofker, K. (2009). Mathematics in India (No. Sirsi)

The essence of mathematics is not to make simple things i9780691120676. Princeton: Princeton University Press.

complicated but to make complicated things simple. [9] R. K. Thakur (1 November 2009). Vedic Mathematics. Unicorn

Mathematics possesses not only truth but supreme and Dragon Books. ISBN 978-81-7806-177-1.

ISSN: 2231-5373 http://www.ijmttjournal.org Page 287

6.
International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017

[10] Rakshith, T. R., & Saligram, R. (2013, March). Design of high

speed low power multiplier using Reversible logic: A Vedic

mathematical approach. In Circuits, Power and Computing

Technologies (ICCPCT), 2013 International Conference on (pp.

775-781).

[11] Tirtha, S. B. K., Agrawala, V. S., & Agrawala, V. S.

(1992). Vedic mathematics (Vol. 10). Motilal Banarsidass Publ.

ISSN: 2231-5373 http://www.ijmttjournal.org Page 288

[10] Rakshith, T. R., & Saligram, R. (2013, March). Design of high

speed low power multiplier using Reversible logic: A Vedic

mathematical approach. In Circuits, Power and Computing

Technologies (ICCPCT), 2013 International Conference on (pp.

775-781).

[11] Tirtha, S. B. K., Agrawala, V. S., & Agrawala, V. S.

(1992). Vedic mathematics (Vol. 10). Motilal Banarsidass Publ.

ISSN: 2231-5373 http://www.ijmttjournal.org Page 288