# 16 SUTRAS OF VEDIC MATHS PDF DOWNLOAD

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of Puri culled a set of 16 Sutras (aphorisms) and 13 Sub - Sutras (corollaries) This book on Vedic Mathematics seeks to present an integrated approach to. Vedic Math essentially rests on the 16 Sutras, or mathematical formulas, as referred to in the Vedas. Here is more about these 16 Sutras. For more tricks on Vedic Mathematics visit sirochaterfarm.tk 1. Follow us on It consists of 16 Sutras (methods) and 13 sub-sutras (Sub methods). Vedic.

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Vedic Mathematics provides principles of high speed multiplication. discussed 16 Vedic Mathematics Sutra which can be used to increase. Vedic Mathematics(ORIGNAL BOOK) - Ebook download as PDF File .pdf), A list of these main 16 Sutras and of their sub-sutras or corollaries is prefixed in the . field of Vedic Mathematics is supposedly based on 16 one-to- three-word sutras ( aphorisms) in Sanskrit, which they claim can solve all modern mathematical.

X V III. X X III. Paqe No. Bi-quadratic Equations His Holiness, better known among his disciples by the beloved name Jagadguruji or Gurudeva was born of highly learned and pious parents in March, His father, late 13ri P. Ranganath Shastri of the Madras High Court. Jagadguruji, named as Venkatraman in his early days, was an exceptionally brilliant student and invariably won the first place in all the subjects in all the classes throughout his educational career. He passed his matriculation examination from the Madras University in January, , topping the list as usual.

After winning the highest place in the B. Examination, Shri Venkatraman Saraswati appeared at the M. Examination in further seven subjects simul taneously securing the highest honours in all, which is perhaps the all-time world-record of academic brilliance. As a student Venkatraman was marked for his splendid brilliance, superb retentive memory and ever-insatiable curiosity.

He would deluge his teachers with myriads of piercing questions which made them uneasy and forced them frequently to make a frank confession of ignorance on their part. In this respect, he was considered to be a terribly mischievous student. Even from his University days Shri Venkatraman Saraswati had started contributing learned articles on religion, philosophy, sociology, history, politics, literature etc.

In fact, study of the latest researches and discoveries in modern science continued to be Shri Jagadgurujis hobby till his vMty last days. Although, however, on the one hand, Prof. Venkatraman Saraswati had acquired an endless fund of learning and his desire to learn ever more was still unquenchable and on the other hand the urge for selfless service of humanity swayed his heart mightily, yet the undoubtedly deepest attraction that Venkatraman Saraswati felt was that towards the study and practice of the science of sciencesthe holy ancient Indian spiritual science or Adhyatma-Vidya.

In , therefore, he proceeded to the Sringeri Math in Mysore to lay himself at the feet of the renowned late Jagadguru Shankaracharya Maharaj Shri Satchidananda Sivabhinava Nrisimha Bharati Swami: But he had not stayed there long, before he had to assume the post of the first Principal of the newly started National College at Rajmahendri under a pressing and clamant call of duty from the nationalist leaders.

Venkatraman Saras wati continued there for three years but in he could not resist his burning desire for spiritual knowledge, practice and attainment any more and, therefore, tearing himself off suddenly from the said college he went back to Shri Satchidananda Sivabhinava Nrisimha Bharati Swami at Sringeri. The next eight years he spent in the profoundest study of the most advanced Vedanta Philosophy and practice of the Brahma-sadhana. During these days Prof. Venkatraman used to study Vedanta at the feet of Shri Nrisimha Bharati Swami, teach Sanskrit and Philosophy in schools there, and practise the highest and most vigorous Yoga-sadhana in the nearby forests.

Frequently, he was also invited by several institutions to deliver lectures on philosophy; for example he delivered a series of sixteen lectures on Shankaracharyas Philosophy at Shankar Institute of Philosophy, Amahier Khandesh and similar lectures at several other places like Poona, Bombay etc. After several years of the most advanced studies, the deepest meditation, and the highest spiritual attainment Prof.

Within two years of his. Immediately, on assuming the pontificate Shri Jagadguruji started touring India from corner to corner and delivering lectures on Sanatana Dharma and by his scintillating intellectual brilliance, powerful oratory, magnetic personality, sincerity of purpose, indomitable will, purity of thought, and loftiness of character he took the entire intellectual and religious class of the nation by storm. Shri Jagadguruji continued to resist his importunate requests for a long time but at last when Jagadguru Shri Madhu sudan Tirthas health took a serious turn in he virtually forced Jagadguru Shri Bharati Krishana Tirthaji to accept the Govardhan Maths Gadi and accordingly Jagadguruji installed Shri Swarupanandji on the Sharadapeeth Gadi and himself assumed the duties of the ecclesiastical and pontifical head of Sri Govardhan Math, Puri.

In this capacity of Jagadguru Shankaracharya of Govar dhan Math, Puri, he continued to disseminate the holy spiritual teachings o f Sanatana Dharma in their pristine purity all over the world the rest of his life for 35 years. He took upon himself the colossal task o f the renaissance of Indian culture, spreading of Sanatana Dharma, revival of the highest human and moral values and enkindling of the loftiest spiritual enlightenment throughput the world and he dedicated his whole life to this lofty and noble mission.

From his very early days Jagadguruji was aware of the need for the right interpretation of Dharma which he defined as the sum total of all the means necessary for speedily making and permanently keeping all the people, individually as well as collectively superlatively comfortable, prosperous, happy, and joyous in all respects including the physical, mental, intellectual, educational, economic, social, political, psychic, spritual etc.

He was painfully aware o f the escapism of some from their duties under the garb of spiritua lity and of the superficial modern educational varnish, of the others, divorced from spiritual and moral standards. He, therefore, always laid great emphasis on the necessity of har monising the spiritual and the material spheres of daily life.

He also wanted to remove the false ideas, on the one hand, of those persons who think that Dharma can be practised by exclusively individual spiritual Sadhana coupled with more honest bread-earning, ignoring ones responsibility for rendering selfless service to the society and on the other hand of those who think that the Sadhana can be complete by mere service of society even without learning or practising any spirituality oneself.

He wanted a happy blending of both. With these ideas agitating his mind for several decades he went on carrying on a laborious, elaborate, patient and dayand-night research to evolve finally a splendid and perfect scheme for all-round reconstruction first of India and through it of the world. The Administrative Board of the Sangha consisted of Jagadgurujis disciples, devotees and admi rers of his idealistic and spiritual ideals for humanitarian service and included a number of high court judges, ministers, educa tionists, statesmen and other personage of the highest calibre viii pleasure.

To see him was a privilege. To speak to him was a real blessing and to be granted a special interview Ah! The magnetic force of his wonderful personality was such that one word, one smile, or even one look was quite enough to convert even the most sceptic into his most ardent and obedient disciple.

He belonged to all irrespective of caste or creed and he was a real Guru to the whole world. People of all nationalities, religions and climes, Brahmins and non-Brahmins, Hindus and Mahomedans, Parsis and Chris tians, Europeans and Americans received equal treatment at the hands of Mis Holiness.

That was the secret of the immense popularity of this great Mahatma. He was grand in his simplicity. People would give any thing and everything to get his blessings and he would talk wdrds of wisdom as freely without fear or favour. He was most easily accessible to all. Thousands of people visited him and prayed for the relief of their miseries. He would actually shed tears when he found people suffering and would pray to God to relieve their suffering.

He was mighty in his learning and voracious in his reading. A sharp intellect, a retentive memory and a keen zest went to mark him as the most distinguished scholar of his day. His leisure moments he would never spend in vain.

He was always reading something or repeating something. There was no branch of knowledge which he did not know and that also shastrically. He was equally learned in Chandahsastra, Ayurveda and Jyotish Sastra. He was a poet of uncommon merit and wrote a number of poems in Sanskrit in the praise of his guru, gods and godesses with a charming flow of Bhakti so conspicuous in all his writings. I have got a collection of over three thousand slokas for ming part of the various eulogistic poems composed by Gurudeva in adoration of various Devas and Devis.

These Slokas have been edited and are being translated into Hindi. They are proposed to be published in three volumes along with Hindi translation. The book on Sanatana Dharma by H. Above all, his Bhakti towards his Vidyaguru was some thing beyond description. He would talk for days together about the greatness of his Vidyaguru. He would be never tired of worshipping the Guru. His Guru also was equally attached to him and called our Swamiji as the own son of the Goddess of Learning, Shri Sarada.

Everyday he would first worship his gurus sandals. His Gurupaduka Stotra clearly indicates the qualities he attributed to the sandals of his guru. Nothing was impossible for him. Above all he was a true Samnyasin.

He held the world but as a stage where every one had to play a part. In short, he was undoubtedly a very great Mahatma but without any display of mysteries or occultisms. I have not been able to express here even one millionth part of what I feel. His spotless holiness, his deep piety, his endless wisdom, his childlike peacefulness, sportiveness and innocence and his universal affection beggar all description.

His Holiness has left us a noble example of simplest living and highest thinking. May all the world benefit by the example of a life so nobly and so simply, so spiritually and so lovingly lived.

Introductory Remarks on the Present Volume I now proceed to give a short account of the genesis of the work published herewith. Obviously these formulae are not to be found in the present recensions of Atharvaveda ; they were actually reconstructed, on the basis of intuitive revelation, from materials scattered here and there in the Atharvaveda.

Revered Gurudeva used to say that he had written sixteen volumes one for each Sutra on these Sutras and that the manuscripts of the said volumes were deposited at the house of one of his disciples.

Unfortunately, the said manuscripts were lost irretrievably from the place of their deposit and this colossal loss was finally confirmed in Revered Gurudeva was not much perturbed over this irretrievable loss and used to say that everything was there in his memory and that he could re-write the 16 volums!

My late husband Sri C. Trivedi, Hon. Secertary V. Sangh noticed that while Sri Jagadguru Maharaj was busy demonstrating before learned people and societies Vedic Mathematics as discovered and propounded by him, some persons who had grasped a smattering of the new Sutras had already started to dazzle audiences as prodigies claiming occult powers without aknowledging indebtedness to the Sutras of Jagadguruji.

My husband, therefore, pleaded earnestly with Gurudeva and persuaded him to arrange for the publication of the Sutras in his own name.

In , when he had decided finally to undertake a tour of the U. This volume was written in his old age within one month and a half with his failing health and weak eyesight. He had planned to write subsequent volu mes, but his failing health and cataract developed in both eyes did not allow the fulfilment of his plans. Now the present volume is the only work on Mathematics that has been left over by Revered Guruji; all his other writings on Vedic Mathematics have, alas, been lost for ever.

The typescript of the present volume was left over by Revered Gurudeva in U. He xi had been given to understand that he would have to go to the U.

But his health deteriorated after his return to India and finally the typescript was brought back from the U. Omkarnath Thakur. I am indebted to Dr. Thakur for this introduction. My hearty and reverent thanks are due to Dr. It is my pleasant duty to offer my heartfelt gratitude to Dr. But for her hard labour which she has undertaken out of a sheer sense of reverence for the noble and glorious work of Revered Gurudeva this volume would not have seen the light of the day for a long time.

My sincere thanks are also due to Sri S. Nijabodha of the Research Section under the charge of Dr.

## Vedic Mathematics(ORIGNAL BOOK)

Sharma, who has ably assisted her in this onerous task. The Humblest of His t isciples Nagpur, 16th March, In the course of our discourses on manifold and multifarious subjects spiritual, metaphysical, philosophical, psychic, psychological, ethical, educational, scientific, mathe matical, historical, political, economic, social etc.

The very word Veda has this derivational meaning i. This derivation, in effect, means, connotes and implies that the Vedas should contain within themselves all the knowledge needed by mankind relating not only to the so-called spiritual or other-worldly matters but also to those Usually described as purely secular , temporal , or wotdly ; and also to the means required by humanity as such for the achievement of all-round, complete and perfect success in all conceivable directions and that there can be no adjectival or restrictive epithet calculated or tending to limit that knowledge down in any sphere, any direction or any respect whatsoever.

It is thus in the fitness of things that the Vedas include i Ayurveda anatomy, physiology, hygiene, sanitary science, medical science, surgery etc.

All these subjects, be it noted, are inherent parts of the Vedas i. Similar is the case with regard to the Vedangas i. Religious study. There were, too, certain personal historical reasons why in our quest for the discovering of all learning in all its departments, branches, sub-branches etc. And the contemptuous or, at best patronising attitude adopted by some so-called Orientalists, Indologists, anti quarians, research-scholars etc.

And we were agreeably astonished and intensely gra tified to find that exceedingly tough mathematical problems which the mathematically most advanced present day Wes tern scientific world had spent huge lots of time, energy and money on and which even now it solves with the utmost difficulty and after vast labour involving large numbers of difficult, tedious and cumbersome steps of working can be easily and readily solved with the help of these ultra-easy Vedic Sutras or mathe matical aphorisms contained in the Parisista the Appendixportion of the A t h a r v a v e d a in a few simple steps and by methods which can be conscientiously described as mere mental arithmetic.

Eversince i. We were thus at last enabled to succeed in attracting the more than passing attention of the authorities of several Indian universities to this subject.

And, consequently, the educationists and the cream of the English educated section of the people including the highest officials e. And not only the newspapers but even the Universitys official reports described the tremendous sensation caused thereby in superlati vely eulogistic terms ; and the papers began to refer to us as the Octogenarian Jagadguru Shankaracharya who had taken Nagpur by storm with his Vedic mathematics , and so on!

It is manifestly impossible, in the course of a short note in the nature of a trailer , to give a full, detailed, tho rough-going, comprehensive and exhaustive description of the unique features and startling characteristics of all the mathematical lore in question.

This can and will be done in the subsequent volumes of this series dealing seriatim and in extenso with all the various portions of all the various branches of mathematics. We may, however, at this point, draw the earnest attention of every one concerned to the following salient items thereof: i The Sutras aphorisms apply to and cover each and every part of each and every chapter of each and every branch of mathematics including ari thmetic, algebra, geometryplane and solid, trigo nometryplane and spherical, conicsgeometrical and analytical, astronomy, calculusdifferential and integral etc.

In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction ; ii The Sutras are easy to understand, easy to apply and easy to remember ; and the whole work can be truthfully summarised in one word mental!

And little children of only 10 or 12 years of age merely look at the sums written on the blackboard on the platform and immediately shout out and dictate the answers from the body of the convocation hall or other venue of the demonstration. And this is because, as a matter of fact, each digit automa tically yields its predecessor and its successor! And we invariably answer and say : 4 is both. It is It magic until you understand i t ; and it is mathematics thereafter ; and then we proceed to substantiate and prove the correctness of this reply of ours!

And vi As regards the time required by the students for mastering the whole course of Vedic mathematics as applied to all its branches, we need merely state from our actual experience that 8 months or 12 months at an average rate of 2 or 3 hours per day xviii should suffice for completing the whole course of mathematical studies on these Vedic lines instead of 15 or 20 years required according to the existing systems of the Indian and also of foreign uni versities.

In this connection, it is a gratifying fact that unlike some so-called Indologists of the type hereinabove referred to there have been some great modem mathematicians and his torians of mathematics like Prof.

Halstead, Professor Ginsburg, Prof. De Moregan, Prof.

Hutton etc. The following few excerpts from the published writings of some universally acknowledged authorities in the domain of the history of mathematics, will speak eloquently for themselves: i On page 20 of his book On the Foundation and Technique of Arithmetic , we find Prof.

Halstead saying The importance of the creation of the z e r o mark can never be exaggerated. This giving of airy nothing not merely a local habitation and a name, a picture but helpful power is the characteristic of the Hindu race whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power. Dutta says: The Hindus adopted the decimal scale vary early. The numerical language of no other nation is so scientific and has attained as high a state of perfection as that of the ancient Hindus.

In symbolism they succeeded with ten signs to express any number most elegantly and simply. It is this beauty of the Hindu numerical notation which attrac ted the attention of all the civilised peoples of the world and charmed them to adopt it iii In this very context, Prof.

Ginsburg says: The Hindu notation was carried to Arabia about A. Ka6ka taught Hindu astronomy and mathematics to the Arabian scholars ; and, with his help, they translated into Arabic the Brahma-Sphuta-Siddhanta of Brahma Gupta. The recent discovery by the French savant M. Nau proves that the Hindu numerals were well known and much appreciated in Syria about the middle of the 7th Century A -D.

Dutta further saying : From Arabia, the numerals slowly marched towards the West through Egypt and Northern Arabia; and they finally entered Europe in the 11th Century. The Europeans called them the Arabic notations, because they received them from the Arabs.

But the Arabs themselves, the Eastern as well as the Western, have unanimously called them the Hindu figures. The above-cited passages are, however, in connection with and in appreciation of Indias invention of the Z e r o mark and her contributions of the 7th century A. In the light, however, of the hereinabove given detailed description of the unique merits and characteristic excellences of the still earlier Vedic Sutras dealt with in the 16 volumes of XX this series1, the conscientious truth-loving and truth-telling historians of Mathematics of the lofty eminence of Prof.

De Morgan etc. It is our earnest aim and aspiration, in these 16 volumes1, to explain and expound the contents of the Vedic mathematical Sutras and bring them within the easy intellectual reach of every seeker after mathematical knowledge.

But, at the same time, we often come across special cases which, although classifiable under the general heading in question, yet present certain additional and typical characterestics which render them still easier to solve. And, therefore, special provision is found to have been made for such special cases by means of special Sutras, sub-Sutras, corollaries etc.

And all that the student of these Sutras has to do is to look for the special characteristics in question, recognise the particular type before him and determine and apply the special formula prescribed therefor.

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And, generally speaking it is only in case no special case is involved, that the general formula has to be resorted to. And this process is naturally a little longer. But it need hardly be pointed out that, even then, the longest of the methods according to the Vedic system comes nowhere in respect of length, cumbrousness and tediousness etc. There are still other methods and in the latter system whereby even that very small working can be rendered shorter still!

This and the beatific beauty of the whole scheme.

## 4 thoughts on “Vedic Maths”

To start with, we should naturally have liked to begin this explanatory and illustrative exposition with a few pro cesses in arithmetical computations relating to multiplications and divisions of huge numbers by big multipliers and big divisors respectively and then go on to other branches of mathematical calculation.

But, as we have just hereinabove referred to a parti cular but wonderful type of mathematical work wherein And then we shall take up the other various parts, one by one, of the various branches of mathematical computation and hope to throw sufficient light thereon to enable the students to make their own comparison and contrast and arrive at correct conclusions on all the various points dealt with.

Multiplication : By current method : The Sanskrit Sutra9 Formula is 9 w n By Vedic mental one-line method : N ote: Only the answer is writ ten automatically down by Vrdhwa Tiryak Sutra forwards or back wards. The beauty of Vedic mathematics lies in the fact that it reduces otherwise cumbersome looking calculations in conventional mathematics to very simple ones.

This is so because the Vedic formulae are claimed to be based on the natural principles on which the human mind works. This is a very interesting field and presents some effective algorithms which can be applied to various branches of engineering such as computing, VLSI implementation and digital signal processing.

This paper is organized in following sections: Section II provides overview of the Vedic sutras, section III elaborates on the uses of these sutras, performance of Vedic algorithms is analysed in section IV and last section concludes the paper. Sutras: 1. Ekadhikena Purvena Ginitasamucchayah 2. Nikhilam Navatascharamam Dashatah Gunaksamucchayah 3. Urdhva-tiryagbhyam 4. Paravartya Yojayet Up-sutras: 5. Shunyam Samyasamucchaye 1. Anurupyena 6.

Anurupye Sunyamanyat 2. Shishyate Sheshsamjnah 7.

Sankalana vyavakalanabhyam 3. Adyamadye Nantyamantyena 8. Puranaprranabhyam 4. Kevalaih Saptakam Gunyat 9. Calana — Kalanabhyam 5.

Vestanam Yavadunam 6. Yavadunam Tavadunam Vyastisamashtih 7. Yavadunam Tavadunikutya Varganka Sheshanynkena Charmena ch Yojayet Sopantyadvayamantyam 8.

Antyayordhshakepi Ekanyunena Purvena 9. Antyatoreva www. Samucchayagunitah Vilokanam Lopanasthapanabhyam Gunitasamucchyah samucchayagunitah In the field of engineering most of the researcher are using following sutras, we will describe them briefly: i Nikhilam navata charanam Dashatah, ii Urdhva-tiryakbyham.

The algorithm has its best case in multiplication of numbers, which are nearer to bases of 10, , i. The procedure of multiplication using the Nikhilam involves minimum mental manual calculations, which in turn will lead to reduced number of steps in computation, reducing the space, saving more time for computation.

The numbers taken can be either less or more than the base considered. The mathematical derivation of the algorithm is given below.

## Vedic Maths

Consider two n-bit numbers x and y to be multiplied. This Sutra highlights parallelism in generation of partial products and their summation as depicted in Fig 2. The numbers to be multiplied are written on two consecutive sides of the square as shown in the figure 1. Thus, each digit of the multiplier has a small box common to a digit of the multiplicand. These small boxes are partitioned into two halves by the crosswise lines.

Each digit of the multiplier is then independently multiplied with every digit of the multiplicand and the two digit product is written in the common box. All the digits lying on a crosswise dotted line are added to the previous carry. The least significant digit of the obtained number acts as the result digit and the rest as the carry for the next step.

Carry for the first step i.Venkatraman Saraswati had acquired an endless fund of learning and his desire to learn ever more was still unquenchable and on the other hand the urge for selfless service of humanity swayed his heart mightily, yet the undoubtedly deepest attraction that Venkatraman Saraswati felt was that towards the study and practice of the science of sciencesthe holy ancient Indian spiritual science or Adhyatma-Vidya.

He had planned to write subsequent volu mes, but his failing health and cataract developed in both eyes did not allow the fulfilment of his plans. Similar is the case with regard to the Vedangas i. But for her hard labour which she has undertaken out of a sheer sense of reverence for the noble and glorious work of Revered Gurudeva this volume would not have seen the light of the day for a long time.

That was the secret of the immense popularity of this great Mahatma. He wanted a happy blending of both. Vedic math reduces the computational steps required to achieve the result.

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