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Kuttaka (Indian Method Of Solving Linear Indeterminate Equations For Integral Solutions)

Kuttaka (Indian Method Of Solving Linear Indeterminate Equations For Integral Solutions)
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Item Code: NAE516
Author: Prof. Venkatesha Murthy
Publisher: Rashtriya Sanskrit Vidyapeetha
Language: English
Edition: 2004
Pages: 64
Cover: Paperback
Other Details: 8.5 inch X 5.5 inch
weight of the book: 92 gms
About The Book

All the regions of human society beyond geographical limitations accept that Sanskrit is the main spring of a grand series of scientific disciplines like Mathematics, Physics, Chemistry. Botany, Meteorology Management etc., have their clean traces back in the ancient Sanskrit literature. Hence emerged the new branch “Sanskrit-Science” with millennia’s strength as a result of the uncessant efforts of modern knowledge seekers all over the world.

Knowledge of Sanskrit and perceptive analysis of scientific knowledge base presented by our Rishis and perceptive thinkers would be of great help in getting a good insight into our rich scientific heritage.

It is the responsibility of our institutions to arouse the interest of younger generations in Sanskrit by unraveling the profound scientific wisdom that is contained in the Sanskrit literature by demonstrating its glory and relevance to the modern world. It is with this objective in view the Sanskrit – Science Study Centre of Rashtriya Sanskrit Vidyapeetha has taken initiative to launch a series of publication of small booklets which would cover a wide canvass of foresaid discipline of Sanskrit – Science.

About The Author

Prof. Venkatesha Murthy, a profound scholar of Mathematics did his M.Sc. (Maths) in the University of Mysore and has worked as Principal of Kendriya Vidyalaya at different places. He retired as the Educational Officer from Kendriya Vidyalaya Sangathan of Bangalore region.

Prof. Venkatesha Murthy has been researching Indian Mathematics and its use in Education for more than twenty years and has conducted several work-shops and seminars on the subject.

Other books by the author are “ Glimpses of Mathematics from the Sanskrit works”, “Numbers and Numerals in Sanskrit works”, “Kuttaka”, Bhavana Mattu Chakravala” (in Kannada) and “Samskruta Grandhgalalli Samkhyagalu Mattu Samkhyasuchakagalu” (in Kannada).

Presently he is working as Dean of Mathematics in the International Academy for Creative Teaching at Bangalore and is a member of Sanskrit-Science Study Centre of Rashtriya Sanskrit Vidyapeetha, Tirupati.

Foreword

It is now being increasingly recognized that ancient Sanskrit Literature contains profound wisdom of physical and social sciences. The scientific knowledge base presented by our Rishis and perceptive thinkers covers a wide canvas of subjects such as Physics, Chemistry, Mathematics, Astronomy, Metallurgy, Bio-Technology and Environmental Science etc.

Unfortunately, due to a very long period of intellectual domination of the forces from outside the region, we have lost our awareness about the profound contributions made by our ancestors that are hidden in the vast Sanskrit literature. Our continued apathy towards Sanskrit language over the recent centuries has also contributed to our lack of awareness about rich scientific heritage. Our ignorance about the richness of our heritage has made us to lose our sense of pride for what is ours. As a result of all this, our sense of confidence in our own capabilities has also been shaken.

Knowledge of Sanskrit and perceptive analysis of contents of our ancient Sanskrit literature would be of great help in getting a good insight into our rich scientific heritage. It is the responsibility of Sanskrit institutions to arouse the interests of the modern world in Sanskrit by unraveling the profound scientific wisdom that is contained in the Sanskrit literature and by demonstrating its relevance to the modern world. It is only when for dealing with the contemporary challenges of life would be a link between the Sanskrit world and the modern world is established that the acceptability of Sanskrit as a relevant subject for dealing with the contemporary challenges of life would be enhanced. It is with this object in view that the Rashtriya Sanskrit Vidyapeetha, Tirupati, launched a series of publication of small book-lets which cover wide convass of subjects such as Physics, Chemistry, Astronomy and Ayurveda etc. for the enlightenment of younger generations of India.

Sri Venkatesha Murthy, who is profound scholar of Mathematics and member of our Sanskrit - Science Study Centre, has prepared this booklet with his vast experience of teaching of Vedic Mathematics and conducting the seminars, workshops and exhibitions related to the subject. I congratulate him for preparing such a wonderful booklet. I hope that this booklet would be found useful by students and scholars alike and inspire many students of Mathematics.

Preface

We feel immensely happy and proud to present this small booklet entitled Kuttaka, Indian Method of Solving Linear Indeterminate Equations for Integral Solutions to the young readers who have a longing to have a glimpse of the wisdom of ancient India.

There is a general belief that contribution of ancient India is limited to the field of humanities particularly that of religion and philosophy. Of course, no other civilization can claim superiority over what India has achieved in that area, Still if we go through the pages of this small book let, we will realize that in the area of Astronomy India’s contribution was amazing. Now India has already lost much of its ancient lore due to the impact of foreign invasion. What remains also is largely unknown as most of it is in Sanskrit. Hence, we feel that there is an urgent need to save the remaining knowledge and build up awareness in all concerned especially among younger generations who are not aware of our ancient scientific heritage contained in Sanskrit.

Shouldering this responsibility i.e. creating the interests among the younger generations in Sanskrit by contained in the Sanskrit literature and demonstrating its relevance to the modern world, Rashtriya Sanskrit Vidyapeetha took the initiative of organizing the Sanskrit Science exhibitions, publishing and propagating the Scientific literature of Sanskrit through out India.

I should mention at the out set that the inspiration to publish such booklets came from our Hon able Chancellor Dr.V.R. Panchamukhi, Economist of international fame, and versatile scholar in Sanskrit.

I would like to express my sincere thanks to Sri Venkatesha Murthy for preparing this wonderful booklet.

If this small booklet kindles a tiny flame of desire in the hearts of young readers for studying the Sanskrit, the storehouse past glory of India. We feel we would have been rewarded for our efforts.

Contents

Introduction1
Chapter 1Kuttaka
1. "Kuttaka Method of Bhascara - II4
1.1 Rules for finding integral solutions. Example 15
1.2 Sub-Rule 1: Division for obtaining a pair of integral values(x,y) for by = ax+c12
1.3 Sub-Rule 2 for obtaining values for negative addend from the values of positive addend. Example 213
1.4 Sub-Rules 3 & 4: when the number of quotients is (i) an even number or17
(ii) an odd number. Example 319
1.5 Sub-rules 5&6: for finding integral multiplier and quotent when
(a) Reduced dividend and reduced addend, and22
(b) Reduced diviser and reduced addend have common factors. Example 424
1.6 Sub-Rule 7: to find many integral solutions28
1.7 Sub-Rule 8: When dividend is a negative integer29
1.8 Sub-Rule 9: When divisor is s negative integer33
Chapter 2Constant Pulverizer37
2.1 Rule for solving linear indeterminate equations using the addend139
Chapter 345
3.1 A General Method for solving Linear Indeterminate Equations for Integral Solutions. Example648
Appendix
method of Joseph Louise Language (1736-1813)53
Epilogue56

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