Contributed by:

This PDF contains :

1. Introduction,

2. Objectives and Methodology,

3. Definitions of Key Terms Used,

4. Analysis,

4.1. Base,

4.2. Complement,

4.3. Ideas for Determination of Complement Number,

4.4. Documents Analysis,

4.5. Interpretation,

5. Results,

6. Conclusions,

Acknowledgments,

References.

1. Introduction,

2. Objectives and Methodology,

3. Definitions of Key Terms Used,

4. Analysis,

4.1. Base,

4.2. Complement,

4.3. Ideas for Determination of Complement Number,

4.4. Documents Analysis,

4.5. Interpretation,

5. Results,

6. Conclusions,

Acknowledgments,

References.

1.
Open Access Library Journal

2020, Volume 7, e6665

ISSN Online: 2333-9721

ISSN Print: 2333-9705

A Thematic Analysis on Vedic

Mathematics and Its

Sher Singh Raikhola1, Dinesh Panthi2*, Eka Ratna Acharya3, Kanhaiya Jha4

Department of Mathematics, Bhaktapur Multiple Campus, Tribhuvan University, Bhaktapur, Nepal

Department of Mathematics, Valmeeki Campus, Nepal Sanskrit University, Kathmandu, Nepal

Central Department of Education, Tribhuvan University, Kathmandu, Nepal

School of Science, Kathmandu University, Dhulikhel, Nepal

How to cite this paper: Raikhola, S.S., Abstract

Panthi, D., Acharya, E.R. and Jha, K. (2020)

A Thematic Analysis on Vedic Mathematics Vedic mathematics is found to be very effective and sound for mental calcula-

and Its Importance. Open Access Library tions in mathematics. Sutras and sub sutras have beautiful and striking tricks

Journal, 7: e6665. for fast and easy for mathematical calculations. In this article, we explore on

importance of Vedic Mathematics with thematic analysis. Vedic Math pro-

Received: July 26, 2020 vides more systematic, simplified, unified and faster than the conventional

Accepted: August 25, 2020 system. A significant and interesting invention which has led to various ap-

Published: August 28, 2020

plications in all the disciplines is the development of Vedic Math approach.

Copyright © 2020 by author(s) and Open

The importance of Vedic mathematics can be characterized as: 1) mathemat-

Access Library Inc. ical calculations, 2) speed, 3) classic approach, 4) fun and interesting, and 5)

This work is licensed under the Creative individual confidence.

Commons Attribution International

License (CC BY 4.0).

Subject Areas

Open Access Numerical Mathematics

Keywords

Vedic Math, Mathematical Calculations, Classic Approach, Vedic Sutra,

NVivo 12 Pro, FFT

1. Introduction

The Sanskrit word “Veda” means knowledge. The word Veda literarily means

the fountain head and illimitable knowledge store. Therefore, the Veda contains

all knowledge that is essential for mankind. Veda is the original word for Vedic.

The word Veda also refers to the sacred ancient Hindu literature which is di-

DOI: 10.4236/oalib.1106665 Aug. 28, 2020 1 Open Access Library Journal

2020, Volume 7, e6665

ISSN Online: 2333-9721

ISSN Print: 2333-9705

A Thematic Analysis on Vedic

Mathematics and Its

Sher Singh Raikhola1, Dinesh Panthi2*, Eka Ratna Acharya3, Kanhaiya Jha4

Department of Mathematics, Bhaktapur Multiple Campus, Tribhuvan University, Bhaktapur, Nepal

Department of Mathematics, Valmeeki Campus, Nepal Sanskrit University, Kathmandu, Nepal

Central Department of Education, Tribhuvan University, Kathmandu, Nepal

School of Science, Kathmandu University, Dhulikhel, Nepal

How to cite this paper: Raikhola, S.S., Abstract

Panthi, D., Acharya, E.R. and Jha, K. (2020)

A Thematic Analysis on Vedic Mathematics Vedic mathematics is found to be very effective and sound for mental calcula-

and Its Importance. Open Access Library tions in mathematics. Sutras and sub sutras have beautiful and striking tricks

Journal, 7: e6665. for fast and easy for mathematical calculations. In this article, we explore on

importance of Vedic Mathematics with thematic analysis. Vedic Math pro-

Received: July 26, 2020 vides more systematic, simplified, unified and faster than the conventional

Accepted: August 25, 2020 system. A significant and interesting invention which has led to various ap-

Published: August 28, 2020

plications in all the disciplines is the development of Vedic Math approach.

Copyright © 2020 by author(s) and Open

The importance of Vedic mathematics can be characterized as: 1) mathemat-

Access Library Inc. ical calculations, 2) speed, 3) classic approach, 4) fun and interesting, and 5)

This work is licensed under the Creative individual confidence.

Commons Attribution International

License (CC BY 4.0).

Subject Areas

Open Access Numerical Mathematics

Keywords

Vedic Math, Mathematical Calculations, Classic Approach, Vedic Sutra,

NVivo 12 Pro, FFT

1. Introduction

The Sanskrit word “Veda” means knowledge. The word Veda literarily means

the fountain head and illimitable knowledge store. Therefore, the Veda contains

all knowledge that is essential for mankind. Veda is the original word for Vedic.

The word Veda also refers to the sacred ancient Hindu literature which is di-

DOI: 10.4236/oalib.1106665 Aug. 28, 2020 1 Open Access Library Journal

2.
S. S. Raikhola et al.

vided into four parts: the Rig-Veda, the Yajur Veda, the Sam Veda and the

Atharva Veda. The Atharva Veda is sometimes called the “Veda of magical for-

mulae”. It is the primary source of information about Vedic culture. Subjects

covered in the Vedas include Grammar, Astronomy, Architecture, Psychology,

Philosophy, Economics, Medicine and Archery [1].

“Vedic Mathematics” is a very good technique or method of calculations

based on simple rule and principles. By this technique, any mathematical prob-

lem whether it is arithmetic or algebra or geometry or trigonometric can be

solved [2].

Vedic mathematics is an old technique that consists of sixteen sutras and thir-

teen sub sutras. It simplifies the fundamental arithmetic operations. It also solves

algebraic concepts like simultaneous equation, quadratic equations, factorization

of cubic equations etc. more effectively than the traditional approach. Vedic

Mathematics can speed up mathematical calculations such as Arithmetic, Alge-

bra, Trigonometry and Geometry. It reduces the time to solve a mathematical

problem and boosts the student confidence [3].

Vedic Mathematics works faster in areas of Trigonometry, Co-ordinate Geo-

metry and Calculus, in the same effective manner. It helps students in minimiz-

ing careless mistakes. It is simple and one-line approach. Moreover, it has an

inbuilt system of a series of checks. Medical research has proved that our brain

weight may increase by five percent if we do not have mental exercise and brain

weight once increased, cannot be reduced [4].

According to a study conducted some years ago, by a university in America,

the constant use of calculators for more than twenty years by a person atrophies

his brain significantly. Through Vedic Mathematics, we use both parts of our

brain, thereby, keeping us mentally fit [5].

Vedic mathematics is an old system of Mathematics. Vedic mathematics was

rediscovered early in early twentieth century by Sri Bharati Krishna Tirthji [6].

Vedic mathematics is known to be the ancient system in Indian mathematics

which was re-explored Vedas in 18th to 19th Century by Sri Bharati Krishna Tirtha-

ji. He developed sixteen sutras (formulae) and thirteen sub-sutras (sub-formula)

to understand the mathematics. In Sanskrit, the terms sutra means “Thread of

Knowledge”. In English, sutra means formula. Swami Bharati Krishna Tirthji

developed methods and techniques for amplifying the principles contained in

the aphorisms and their corollaries, and called it Vedic Mathematics [7].

Vedic mathematics [6] is useful for basic and complex mathematical opera-

tions. The methods provided in the book for basic mathematics are easy but po-

werful. Large calculation on division, multiplications, addition, and subtraction

can be performed easily by using Vedic tricks and formulae. Vedic Sutras and

tricks provide beautiful and striking methods that is systematic than modern

system of mathematics. Vedic mathematics provides the integrated structure of

mathematics that is complementary, direct and easy. The Vedic system allows

children to use these principles to simplify a math problem to a level that they

DOI: 10.4236/oalib.1106665 2 Open Access Library Journal

vided into four parts: the Rig-Veda, the Yajur Veda, the Sam Veda and the

Atharva Veda. The Atharva Veda is sometimes called the “Veda of magical for-

mulae”. It is the primary source of information about Vedic culture. Subjects

covered in the Vedas include Grammar, Astronomy, Architecture, Psychology,

Philosophy, Economics, Medicine and Archery [1].

“Vedic Mathematics” is a very good technique or method of calculations

based on simple rule and principles. By this technique, any mathematical prob-

lem whether it is arithmetic or algebra or geometry or trigonometric can be

solved [2].

Vedic mathematics is an old technique that consists of sixteen sutras and thir-

teen sub sutras. It simplifies the fundamental arithmetic operations. It also solves

algebraic concepts like simultaneous equation, quadratic equations, factorization

of cubic equations etc. more effectively than the traditional approach. Vedic

Mathematics can speed up mathematical calculations such as Arithmetic, Alge-

bra, Trigonometry and Geometry. It reduces the time to solve a mathematical

problem and boosts the student confidence [3].

Vedic Mathematics works faster in areas of Trigonometry, Co-ordinate Geo-

metry and Calculus, in the same effective manner. It helps students in minimiz-

ing careless mistakes. It is simple and one-line approach. Moreover, it has an

inbuilt system of a series of checks. Medical research has proved that our brain

weight may increase by five percent if we do not have mental exercise and brain

weight once increased, cannot be reduced [4].

According to a study conducted some years ago, by a university in America,

the constant use of calculators for more than twenty years by a person atrophies

his brain significantly. Through Vedic Mathematics, we use both parts of our

brain, thereby, keeping us mentally fit [5].

Vedic mathematics is an old system of Mathematics. Vedic mathematics was

rediscovered early in early twentieth century by Sri Bharati Krishna Tirthji [6].

Vedic mathematics is known to be the ancient system in Indian mathematics

which was re-explored Vedas in 18th to 19th Century by Sri Bharati Krishna Tirtha-

ji. He developed sixteen sutras (formulae) and thirteen sub-sutras (sub-formula)

to understand the mathematics. In Sanskrit, the terms sutra means “Thread of

Knowledge”. In English, sutra means formula. Swami Bharati Krishna Tirthji

developed methods and techniques for amplifying the principles contained in

the aphorisms and their corollaries, and called it Vedic Mathematics [7].

Vedic mathematics [6] is useful for basic and complex mathematical opera-

tions. The methods provided in the book for basic mathematics are easy but po-

werful. Large calculation on division, multiplications, addition, and subtraction

can be performed easily by using Vedic tricks and formulae. Vedic Sutras and

tricks provide beautiful and striking methods that is systematic than modern

system of mathematics. Vedic mathematics provides the integrated structure of

mathematics that is complementary, direct and easy. The Vedic system allows

children to use these principles to simplify a math problem to a level that they

DOI: 10.4236/oalib.1106665 2 Open Access Library Journal

3.
S. S. Raikhola et al.

can master and build their “Number Sense”. Calculating in Vedic Mathematics

is like playing mind game and results can be digging out very shortly like read-

ing words. The book provides varieties of sutras (formulas) to solve mathemati-

cal problems in a creative, interesting and intelligent way. It will support to take

advantage in mathematics and logic that help our children to excel in the class-

room and beyond [8]. It can induce creativity in intelligent pupils, while helping

slow-learners grasp the basic concepts of mathematics. A wider use of Vedic

math can undoubtedly generate interest in a subject that is generally dreaded by

children [9].

Vedic Mathematics [6] contains 16 formulas and 13 sub-formulas. These su-

tras are used in solving complex computations, and executing them manually.

The algorithms and principles are given in Urdhvatiryakbhyam sutra is used for

vertical and crosswise multiplication [10]. Vedic multiplier is based upon this

sutra. Array multiplication is its primary source. In the design and implementa-

tion of Triyakbhyam were done and the speed was compared with Nikhilam su-

tra, squaring and cubing algorithm [5].

2. Objectives and Methodology

Bajaj argued Vedic Mathematics allows increasing people’s confidence by ap-

plying Sutra to solve the mathematical problems [4]. It also suggested creativity

to calculate problems that is related to Vedic Mathematics. Agarwal, Matta and

Aryafound Vedic mathematics is an efficient algorithm for speedy calculations

of math problems [2]. So, in this regard, this study has been carried out to study

about the Vedic Mathematics and its importance in the mathematics. That is

why, the researchers showed interest to undertake this research. The qualitative

research aims to discover the meaning through the patterns of observed infor-

mation. It emerges after the keen observation, proper documentation and careful

analysis of the research topic. This study has set the objectives to find out the

importance of Vedic Math in the modern era to make a word cloud of Vedic

Mathematics.This study mainly focuses on Vedic Mathematics and its impor-

tance in modern era. In order to explore the importance of Vedic Mathematics,

the researcher has collected literature explaining the importance of Vedic ma-

thematics.

The researchers used thematic analysis approach to analyze the available lite-

ratures to highlight the major theme of contribution of Vedic mathematics in

the modern era. Researchers collected published works as its data and subjects

them to a careful analysis that usually includes qualitative aspects. NVivo 12 Pro

software is used for qualitative analysis for Thematic Analysis. World Cloud and

Cluster Analysis is made to show the major theme of Vedic Math’s importance

in the modern era. Thematic analysis through word cloud gives importance of

Vedic mathematics can be characterized as 1) mathematical calculations, 2)

speed, 3) classic approach, 4) fun and interesting, and 5) individual confidence.

Hence this is an exploratory study to generate theme.

DOI: 10.4236/oalib.1106665 3 Open Access Library Journal

can master and build their “Number Sense”. Calculating in Vedic Mathematics

is like playing mind game and results can be digging out very shortly like read-

ing words. The book provides varieties of sutras (formulas) to solve mathemati-

cal problems in a creative, interesting and intelligent way. It will support to take

advantage in mathematics and logic that help our children to excel in the class-

room and beyond [8]. It can induce creativity in intelligent pupils, while helping

slow-learners grasp the basic concepts of mathematics. A wider use of Vedic

math can undoubtedly generate interest in a subject that is generally dreaded by

children [9].

Vedic Mathematics [6] contains 16 formulas and 13 sub-formulas. These su-

tras are used in solving complex computations, and executing them manually.

The algorithms and principles are given in Urdhvatiryakbhyam sutra is used for

vertical and crosswise multiplication [10]. Vedic multiplier is based upon this

sutra. Array multiplication is its primary source. In the design and implementa-

tion of Triyakbhyam were done and the speed was compared with Nikhilam su-

tra, squaring and cubing algorithm [5].

2. Objectives and Methodology

Bajaj argued Vedic Mathematics allows increasing people’s confidence by ap-

plying Sutra to solve the mathematical problems [4]. It also suggested creativity

to calculate problems that is related to Vedic Mathematics. Agarwal, Matta and

Aryafound Vedic mathematics is an efficient algorithm for speedy calculations

of math problems [2]. So, in this regard, this study has been carried out to study

about the Vedic Mathematics and its importance in the mathematics. That is

why, the researchers showed interest to undertake this research. The qualitative

research aims to discover the meaning through the patterns of observed infor-

mation. It emerges after the keen observation, proper documentation and careful

analysis of the research topic. This study has set the objectives to find out the

importance of Vedic Math in the modern era to make a word cloud of Vedic

Mathematics.This study mainly focuses on Vedic Mathematics and its impor-

tance in modern era. In order to explore the importance of Vedic Mathematics,

the researcher has collected literature explaining the importance of Vedic ma-

thematics.

The researchers used thematic analysis approach to analyze the available lite-

ratures to highlight the major theme of contribution of Vedic mathematics in

the modern era. Researchers collected published works as its data and subjects

them to a careful analysis that usually includes qualitative aspects. NVivo 12 Pro

software is used for qualitative analysis for Thematic Analysis. World Cloud and

Cluster Analysis is made to show the major theme of Vedic Math’s importance

in the modern era. Thematic analysis through word cloud gives importance of

Vedic mathematics can be characterized as 1) mathematical calculations, 2)

speed, 3) classic approach, 4) fun and interesting, and 5) individual confidence.

Hence this is an exploratory study to generate theme.

DOI: 10.4236/oalib.1106665 3 Open Access Library Journal

4.
S. S. Raikhola et al.

3. Definitions of Key Terms Used

NVivo—NVivo is a Qualitative data analysis (QDA) computer software

package produced Qualitative Research Software (QSR) International.

FFT—A fast Fourier transform (FFT) is an algorithm that computes the dis-

crete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier

analysis converts a signal from its original domain to a representation in the

frequency domain and vice versa.

Thematic Analysis—Actually, thematic analysis (TA) is a well-known me-

thod for analyzing, interpretating, and explaining data in various disciplines and

fields. It has several uses. It can be applied in distinct ways in distinct fields. It is

used to address lots of different research questions. It is one of the cluster of

methods that focus on identifying patterned meaning across a dataset.

TA is best thought of as an umbrella term for a set of approaches for analyzing

qualitative data that share a focus on identifying themes (patterns of meaning) in

qualitative data.

Cluster Analysis—Cluster analysis or clustering is the method of keeping a

set of objects together in such a way that objects in the same group known as

clusters are similar to each other than those from other groups. It’s a prime

function of exploratory data mining and a well-known technique for statistical

data analysis, used in many fields, including pattern recognition, image analysis,

information retrieval, bioinformatics, data compression, computer graphics and

machine learning.

4. Analysis

It is very important to learn and understand the basic concepts to make any cal-

culation easy. These two basic concepts-base and complement are the pillars of

Vedic Mathematics. These are explained below with examples.

4.1. Base

Bases are the numbers which start with 1 and ends with 0’s. For example 10, 100,

1000, 10000, 100000, and so on are called bases. The first 2-digit number is 10

and the first 3-digit number is 100 and so on. Only these kinds of numbers are

considered as bases. Numbers such as 200, 300, 450, 1500 are not considered as

bases.

4.2. Complement

When two numbers are added with each other and it results in the next nearest

base, then they are called Complements of each other.

For Example,

1) Consider the number 74. The next nearest base of 74 is 100. By adding 26

we will get 100. So 74 and 26 are complements to each other.

2) Consider the number 254. The next nearest base of 254 is 1000. By adding

746 we get 1000. So they are Complements to each other.

DOI: 10.4236/oalib.1106665 4 Open Access Library Journal

3. Definitions of Key Terms Used

NVivo—NVivo is a Qualitative data analysis (QDA) computer software

package produced Qualitative Research Software (QSR) International.

FFT—A fast Fourier transform (FFT) is an algorithm that computes the dis-

crete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier

analysis converts a signal from its original domain to a representation in the

frequency domain and vice versa.

Thematic Analysis—Actually, thematic analysis (TA) is a well-known me-

thod for analyzing, interpretating, and explaining data in various disciplines and

fields. It has several uses. It can be applied in distinct ways in distinct fields. It is

used to address lots of different research questions. It is one of the cluster of

methods that focus on identifying patterned meaning across a dataset.

TA is best thought of as an umbrella term for a set of approaches for analyzing

qualitative data that share a focus on identifying themes (patterns of meaning) in

qualitative data.

Cluster Analysis—Cluster analysis or clustering is the method of keeping a

set of objects together in such a way that objects in the same group known as

clusters are similar to each other than those from other groups. It’s a prime

function of exploratory data mining and a well-known technique for statistical

data analysis, used in many fields, including pattern recognition, image analysis,

information retrieval, bioinformatics, data compression, computer graphics and

machine learning.

4. Analysis

It is very important to learn and understand the basic concepts to make any cal-

culation easy. These two basic concepts-base and complement are the pillars of

Vedic Mathematics. These are explained below with examples.

4.1. Base

Bases are the numbers which start with 1 and ends with 0’s. For example 10, 100,

1000, 10000, 100000, and so on are called bases. The first 2-digit number is 10

and the first 3-digit number is 100 and so on. Only these kinds of numbers are

considered as bases. Numbers such as 200, 300, 450, 1500 are not considered as

bases.

4.2. Complement

When two numbers are added with each other and it results in the next nearest

base, then they are called Complements of each other.

For Example,

1) Consider the number 74. The next nearest base of 74 is 100. By adding 26

we will get 100. So 74 and 26 are complements to each other.

2) Consider the number 254. The next nearest base of 254 is 1000. By adding

746 we get 1000. So they are Complements to each other.

DOI: 10.4236/oalib.1106665 4 Open Access Library Journal

5.
S. S. Raikhola et al.

3) Similarly, Complement of 3 is 7(Base is 10), Complement of 28 is 72 (Base

is 100), Complement of 6545 is 3455 (Base is 10000).

4.3. Ideas for Determination of Complement Number

Example: Subtract 3 5 8 7 3 2 from 1000000

To determine the Complement of a number can be calculated by subtracting

all numbers from 9 and the last number by 10, for example; complement of

358732 can be calculate as,

9 9 9 9 9 10 − 3 5 8 7 3 2 = 6 4 1 2 6 8

Or

9 9 9 9 9 10

↓ ↓ ↓ ↓ ↓ ↓

Subtract

3 5 8 7 3 2

= 6 4 1 2 6 8

The Formula is “All from 9 and the last from 10’’ [6]. Similarly, the Comple-

ment of 5183 can be calculate as,

9 9 9 10 − 5 1 8 3 = 4 8 1 7

4.4. Documents Analysis

Documents analysis also supports to thematic analysis. Documents are the relia-

ble sources of data. Vaidya concluded that in Vedic Math approach has time and

again proved to offer a huge advantage in preparation for these events as well as

for an individual’s holistic development [10]. It is useful in bringing back fun

and interest of students in an abstruse subject like Mathematics. A systematic

and developed study of Vedic Mathematics will be extremely useful for students

and researchers.

Acharya made efforts to connect classical and modern approach to change the

archetype in mathematics by focusing upon the indications of mathematical de-

velopments [1]. The author found applications of derivatives in solving quadrat-

ic equation and also explained the relation between the first order derivative and

factors of quadratic expression, cubic expression and bi-quadratic expression. By

giving examples, the author has also explained application of Vertical and

Crosswise Sutra for solving successive differentiation of the product of algebraic

and exponential functions and also for solving problems of Integration based on

Integration by parts. Writer concludes with the help of that evidences that in 100

years before the contents have not significantly changed but algorithm and the

method of solving problem has altered.

Agarwal, Matta, and Arya studied the scheme and method of FFT by applying

an efficient algorithm of Vedic Math which results being speedy and dependable

for calculating N-point Discrete Fourier Transform [2]. Authors have explained

how to reduce algorithm of 4 bit multiplication into 4 bit multiplication by giv-

ing an example by using Urdhva-Tiryagbhyam. They have also discussed about

the design of a particular FFT with the help of Vedic multiplier and adder. When

DOI: 10.4236/oalib.1106665 5 Open Access Library Journal

3) Similarly, Complement of 3 is 7(Base is 10), Complement of 28 is 72 (Base

is 100), Complement of 6545 is 3455 (Base is 10000).

4.3. Ideas for Determination of Complement Number

Example: Subtract 3 5 8 7 3 2 from 1000000

To determine the Complement of a number can be calculated by subtracting

all numbers from 9 and the last number by 10, for example; complement of

358732 can be calculate as,

9 9 9 9 9 10 − 3 5 8 7 3 2 = 6 4 1 2 6 8

Or

9 9 9 9 9 10

↓ ↓ ↓ ↓ ↓ ↓

Subtract

3 5 8 7 3 2

= 6 4 1 2 6 8

The Formula is “All from 9 and the last from 10’’ [6]. Similarly, the Comple-

ment of 5183 can be calculate as,

9 9 9 10 − 5 1 8 3 = 4 8 1 7

4.4. Documents Analysis

Documents analysis also supports to thematic analysis. Documents are the relia-

ble sources of data. Vaidya concluded that in Vedic Math approach has time and

again proved to offer a huge advantage in preparation for these events as well as

for an individual’s holistic development [10]. It is useful in bringing back fun

and interest of students in an abstruse subject like Mathematics. A systematic

and developed study of Vedic Mathematics will be extremely useful for students

and researchers.

Acharya made efforts to connect classical and modern approach to change the

archetype in mathematics by focusing upon the indications of mathematical de-

velopments [1]. The author found applications of derivatives in solving quadrat-

ic equation and also explained the relation between the first order derivative and

factors of quadratic expression, cubic expression and bi-quadratic expression. By

giving examples, the author has also explained application of Vertical and

Crosswise Sutra for solving successive differentiation of the product of algebraic

and exponential functions and also for solving problems of Integration based on

Integration by parts. Writer concludes with the help of that evidences that in 100

years before the contents have not significantly changed but algorithm and the

method of solving problem has altered.

Agarwal, Matta, and Arya studied the scheme and method of FFT by applying

an efficient algorithm of Vedic Math which results being speedy and dependable

for calculating N-point Discrete Fourier Transform [2]. Authors have explained

how to reduce algorithm of 4 bit multiplication into 4 bit multiplication by giv-

ing an example by using Urdhva-Tiryagbhyam. They have also discussed about

the design of a particular FFT with the help of Vedic multiplier and adder. When

DOI: 10.4236/oalib.1106665 5 Open Access Library Journal

6.
S. S. Raikhola et al.

compare to regular Fast Fourier transform, and Vedic FFT is more efficient in

term of time. A combination of FFT and Vedic Mathematics will create new de-

velopments in various fields.

Aggarwal investigated on observations from “Figuring” by Shakuntala Devi

and found Human computers’ like Shakuntala Devi do their mental calculations,

their shortcuts and tips are remarkably similar to the short cuts used in Vedic

Math’s secret steps [3].

Bajaj depicted that when one applies Sutra to certain questions requiring crea-

tivity and rationality, this enhances a person’s self-confidence [4]. The one thing

common among all math prodigies since 15th century is the desire to excel by

developing innovative methods to approach the given problem. In Vedic me-

thodology, solution to any given problem can be arrived at in two different

ways-one being the implementation of the general approach & the other one is

identifying the arrangement of variables and application of situation specific

formulas. As per his opinion, a significant and interesting invention which has

led to various applications in all the disciplines is the development of Vedic Ma-

thematics (VM) approach. This wide applicability can be explained by the quick

& insightful solutions obtained through basic minimum arithmetic procedure.

The author has tried to compare each Vedic Sutra with algebraic proof by pro-

viding sufficient examples.

4.5. Interpretation

Theme Generation: Available review of literature is processed through NVivo 12

Pro and theme is generated as show in Figure 1.

Figure 1 shows the major bold type face as calculating, Vedic, contents,

change, functions, individual, development, sutra, functions, disciplines, ex-

plained, mathematics, useful and so on. World Cloud generates themes as Vedic

math is algebraic functions which solve the given problems and builds the con-

fidence.

Cluster analysis is done through items clustered by word similarity. It is ex-

pressed in Figure 2.

Figure 2 shows that Vedic mathematics is clustered as mathematical calcula-

tions, speed, classic approach, fun and interest, and individual confidence. It is

said that Vedic math calculation creates fund and interest and faster calculates

the solution and increase individual confidence.

The Sutras apply to and cover almost every branch of Mathematics. They are

applied to solve complex problems that involve a large number of mathematical

operations. The proper application of sutra saves time and needs less effort in

solving the problem in comparison to formal methods. As the application of the

sutra is logical and rational, the solutions appear like magic. It’s a matter of sur-

prise to everyone. The computer computation is also based upon these underly-

ing principles. They provide good methods of calculations and proper ways of

thinking for their appropriate applications.

DOI: 10.4236/oalib.1106665 6 Open Access Library Journal

compare to regular Fast Fourier transform, and Vedic FFT is more efficient in

term of time. A combination of FFT and Vedic Mathematics will create new de-

velopments in various fields.

Aggarwal investigated on observations from “Figuring” by Shakuntala Devi

and found Human computers’ like Shakuntala Devi do their mental calculations,

their shortcuts and tips are remarkably similar to the short cuts used in Vedic

Math’s secret steps [3].

Bajaj depicted that when one applies Sutra to certain questions requiring crea-

tivity and rationality, this enhances a person’s self-confidence [4]. The one thing

common among all math prodigies since 15th century is the desire to excel by

developing innovative methods to approach the given problem. In Vedic me-

thodology, solution to any given problem can be arrived at in two different

ways-one being the implementation of the general approach & the other one is

identifying the arrangement of variables and application of situation specific

formulas. As per his opinion, a significant and interesting invention which has

led to various applications in all the disciplines is the development of Vedic Ma-

thematics (VM) approach. This wide applicability can be explained by the quick

& insightful solutions obtained through basic minimum arithmetic procedure.

The author has tried to compare each Vedic Sutra with algebraic proof by pro-

viding sufficient examples.

4.5. Interpretation

Theme Generation: Available review of literature is processed through NVivo 12

Pro and theme is generated as show in Figure 1.

Figure 1 shows the major bold type face as calculating, Vedic, contents,

change, functions, individual, development, sutra, functions, disciplines, ex-

plained, mathematics, useful and so on. World Cloud generates themes as Vedic

math is algebraic functions which solve the given problems and builds the con-

fidence.

Cluster analysis is done through items clustered by word similarity. It is ex-

pressed in Figure 2.

Figure 2 shows that Vedic mathematics is clustered as mathematical calcula-

tions, speed, classic approach, fun and interest, and individual confidence. It is

said that Vedic math calculation creates fund and interest and faster calculates

the solution and increase individual confidence.

The Sutras apply to and cover almost every branch of Mathematics. They are

applied to solve complex problems that involve a large number of mathematical

operations. The proper application of sutra saves time and needs less effort in

solving the problem in comparison to formal methods. As the application of the

sutra is logical and rational, the solutions appear like magic. It’s a matter of sur-

prise to everyone. The computer computation is also based upon these underly-

ing principles. They provide good methods of calculations and proper ways of

thinking for their appropriate applications.

DOI: 10.4236/oalib.1106665 6 Open Access Library Journal

7.
S. S. Raikhola et al.

Figure 1. Word cloud. Source: Output of NVIVO 12 Pro.

Figure 2. Cluster analysis. Source: Output of NVIVO 12 Pro.

This course on Vedic Mathematics aims to bring an integrated approach in

learning mathematics with curiosity of observations and inquisitiveness. It

avoids the monotony of applying traditional theories and working with them

mechanically. The given explanations make the process vivid to the inquisitive

learners. The logical proof of sutras eliminates the common misconceptions that

the sutras are jugglery. The proper applications of sutras have improved the

skills of computations of the learners significantly. It ensures both speed and

accuracy as it is strictly based upon the rational and logical reasoning.

The knowledge of such methods makes the teachers able to shape the stu-

dents’ mind properly and enhance their talent and creativity. Applications of su-

tras to specific problems are not possible without rational thinking. It helps to

sharpen intuition which is bottom line of the mastery of the mathematical ge-

niuses of the past and present like Aryabhatta, Bhaskaracharya, Srinivasa Ra-

manujan, etc.

This course helps to use the above stated sutra and sub-sutras in learning ma-

thematics at the secondary level in a way different from what is taught at

DOI: 10.4236/oalib.1106665 7 Open Access Library Journal

Figure 1. Word cloud. Source: Output of NVIVO 12 Pro.

Figure 2. Cluster analysis. Source: Output of NVIVO 12 Pro.

This course on Vedic Mathematics aims to bring an integrated approach in

learning mathematics with curiosity of observations and inquisitiveness. It

avoids the monotony of applying traditional theories and working with them

mechanically. The given explanations make the process vivid to the inquisitive

learners. The logical proof of sutras eliminates the common misconceptions that

the sutras are jugglery. The proper applications of sutras have improved the

skills of computations of the learners significantly. It ensures both speed and

accuracy as it is strictly based upon the rational and logical reasoning.

The knowledge of such methods makes the teachers able to shape the stu-

dents’ mind properly and enhance their talent and creativity. Applications of su-

tras to specific problems are not possible without rational thinking. It helps to

sharpen intuition which is bottom line of the mastery of the mathematical ge-

niuses of the past and present like Aryabhatta, Bhaskaracharya, Srinivasa Ra-

manujan, etc.

This course helps to use the above stated sutra and sub-sutras in learning ma-

thematics at the secondary level in a way different from what is taught at

DOI: 10.4236/oalib.1106665 7 Open Access Library Journal

8.
S. S. Raikhola et al.

present. The method has become very effective. The innovation in the presenta-

tion is the algebraic proof for every elucidation of the Sutra or the Sub-Sutra

concerned.

5. Results

• Vedic Math provides more systematic, simplified, unified & faster than the

conventional system.

• Vedic Math gives the flexibility, fun and immense satisfaction and converts a

tedious subject into a playful and blissful one which anyone can learn with

smiles.

• Vedic Math with its special features has the inbuilt potential to solve the

psychological problem of Mathematics anxiety.

• Vedic Math increases speed and accuracy. Mathematics, derived from the

Veda, provides one line, mental and super-fast methods along with quick

cross checking systems.

• Vedic mathematics provides the integrated structure of mathematics that is

complementary, direct and easy.

• A significant and interesting invention which has led to various applications

in all the disciplines is the development of Vedic mathematics approach.

6. Conclusions

Vedic Mathematics is easier to learn, faster to use and less prone to error than

conventional methods. Furthermore, the techniques of Vedic Mathematics not

only enable the students to solve specific mathematical problems: they also de-

velop creativity, logical thinking and intuition.

From the above study, we can conclude that modern teaching of one way cal-

culations are rigid and boring. Vedic Mathematics has general methods and also

many methods that apply for special cases. These calculations can often be car-

ried out independent of direction & orientation. Because of this flexibility, stu-

dents can use their own approach which promotes creativity and intuition. In

this rapidly changing world, flexibility and adaptability are indispensible for

success. By using Vedic Sutras, complicated and lengthy computations can be

solved with greater accuracy and lesser time as compared to calculations based

on conventional mathematics. Vedic Mathematics also improves memory and

creates greater mental alertness. The most significant quality of Vedic Mathe-

matics is its consistency. Because of this quality, it creates stress-free and enjoya-

ble environment. It inspires innovations. The beautiful coherence between

arithmetic and algebra is clearly visible in the Vedic system.

Acknowledgements

We would like to thank Dr. Shajeeb Kumar Shrestha, Associate Professor of

Management, of Tribhuvan University, Nepal for assistance with Cluster analy-

sis technique and methodology that greatly improved the manuscript.

DOI: 10.4236/oalib.1106665 8 Open Access Library Journal

present. The method has become very effective. The innovation in the presenta-

tion is the algebraic proof for every elucidation of the Sutra or the Sub-Sutra

concerned.

5. Results

• Vedic Math provides more systematic, simplified, unified & faster than the

conventional system.

• Vedic Math gives the flexibility, fun and immense satisfaction and converts a

tedious subject into a playful and blissful one which anyone can learn with

smiles.

• Vedic Math with its special features has the inbuilt potential to solve the

psychological problem of Mathematics anxiety.

• Vedic Math increases speed and accuracy. Mathematics, derived from the

Veda, provides one line, mental and super-fast methods along with quick

cross checking systems.

• Vedic mathematics provides the integrated structure of mathematics that is

complementary, direct and easy.

• A significant and interesting invention which has led to various applications

in all the disciplines is the development of Vedic mathematics approach.

6. Conclusions

Vedic Mathematics is easier to learn, faster to use and less prone to error than

conventional methods. Furthermore, the techniques of Vedic Mathematics not

only enable the students to solve specific mathematical problems: they also de-

velop creativity, logical thinking and intuition.

From the above study, we can conclude that modern teaching of one way cal-

culations are rigid and boring. Vedic Mathematics has general methods and also

many methods that apply for special cases. These calculations can often be car-

ried out independent of direction & orientation. Because of this flexibility, stu-

dents can use their own approach which promotes creativity and intuition. In

this rapidly changing world, flexibility and adaptability are indispensible for

success. By using Vedic Sutras, complicated and lengthy computations can be

solved with greater accuracy and lesser time as compared to calculations based

on conventional mathematics. Vedic Mathematics also improves memory and

creates greater mental alertness. The most significant quality of Vedic Mathe-

matics is its consistency. Because of this quality, it creates stress-free and enjoya-

ble environment. It inspires innovations. The beautiful coherence between

arithmetic and algebra is clearly visible in the Vedic system.

Acknowledgements

We would like to thank Dr. Shajeeb Kumar Shrestha, Associate Professor of

Management, of Tribhuvan University, Nepal for assistance with Cluster analy-

sis technique and methodology that greatly improved the manuscript.

DOI: 10.4236/oalib.1106665 8 Open Access Library Journal

9.
S. S. Raikhola et al.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this pa-

per.

References

[1] Acharya, E.R. (2015) Mathematics Hundred Years Before and Now. History Re-

search, 3, 41-47. https://doi.org/10.11648/j.history.20150303.11

[2] Agarwal, J., Matta, V. and Arya, D. (2013) Design and Implementation of FFT Pro-

cessor Using Vedic Multiplier with High Throughput. International Journal of

Emerging Technology and Advanced Engineering, 3, 207-211.

[3] Aggrawal, S. (2013) Observations from Figuring. http://vedicmaths.org

[4] Bajaj, R. (2005) Vedic mathematics: The Problem Solver. Black Rose Publications.

[5] Bose, S. (2014) Vedic Mathematics. V and S Publishers, New Delhi, Edition 192.

[6] Tirthaji, S.B.K. (1965) Vedic Mathematics. Motilal Banarasidass, New Delhi.

[7] The Concept of Vedic Maths (2015)

https://www.walnutexcellence.com/the-concept-of-vedic-maths/

[8] William, K. (n.d.) How to Unleash Your Natural Ability for Mental Math by Dis-

covering the “Secret Mathematician” Hidden Deep within You!

http://www.mathmonkeybrunei.com/vedic_math.php

[9] Das, S. (n.d.) The History & Future of Vedic Maths.

http://hinduism.about.com/od/vedicmaths/a/vedicmath_history_future.htm

[10] Vaidya, S.A. (2019) The Contribution of Vedic Mathematics in Advance Calculus.

Doctoral Dissertation, Shri Jagdishprasad Jhabarmal Tibrewala University, Rajast-

han, India.

DOI: 10.4236/oalib.1106665 9 Open Access Library Journal

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this pa-

per.

References

[1] Acharya, E.R. (2015) Mathematics Hundred Years Before and Now. History Re-

search, 3, 41-47. https://doi.org/10.11648/j.history.20150303.11

[2] Agarwal, J., Matta, V. and Arya, D. (2013) Design and Implementation of FFT Pro-

cessor Using Vedic Multiplier with High Throughput. International Journal of

Emerging Technology and Advanced Engineering, 3, 207-211.

[3] Aggrawal, S. (2013) Observations from Figuring. http://vedicmaths.org

[4] Bajaj, R. (2005) Vedic mathematics: The Problem Solver. Black Rose Publications.

[5] Bose, S. (2014) Vedic Mathematics. V and S Publishers, New Delhi, Edition 192.

[6] Tirthaji, S.B.K. (1965) Vedic Mathematics. Motilal Banarasidass, New Delhi.

[7] The Concept of Vedic Maths (2015)

https://www.walnutexcellence.com/the-concept-of-vedic-maths/

[8] William, K. (n.d.) How to Unleash Your Natural Ability for Mental Math by Dis-

covering the “Secret Mathematician” Hidden Deep within You!

http://www.mathmonkeybrunei.com/vedic_math.php

[9] Das, S. (n.d.) The History & Future of Vedic Maths.

http://hinduism.about.com/od/vedicmaths/a/vedicmath_history_future.htm

[10] Vaidya, S.A. (2019) The Contribution of Vedic Mathematics in Advance Calculus.

Doctoral Dissertation, Shri Jagdishprasad Jhabarmal Tibrewala University, Rajast-

han, India.

DOI: 10.4236/oalib.1106665 9 Open Access Library Journal