# VEDIC MATHEMATICS PDF

Mar 18, I may try to edit this book or write a new book in future, reflecting In solar vaia Cambridge International AS and A Level Mathematics Pure. According to him, there has been considerable literature on Mathematics in the Veda-sakhas. Unfortunately most of it has been lost to humanity as of now. PDF | On Apr 1, , Uwe Wystup and others published Vedic Mathematics Teaching an Old Dog New Tricks.

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Views of Prof. ininenzero.cf about Vedic. Mathematics from Frontline. Neither Vedic Nor Mathematics. Views about the Book in Favour and Against. cation of the book Vedic Mathematics or 'Sixteen Simple Mathe- matical Formulae,' by Simple Mathematical Formule from the Vedas' was written by. Vedic Mathematics introduces the wonderful applications to Arithmetical The basis of Vedic mathematics, are the 16 sutras, which attribute a set of qualities to .

The numbers taken can be either less or more than the base considered. The mathematical derivation of the algorithm is given below. 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. Most of the researchers have used the Vedic mathematics method such as multiplication, division, squares and cubes in above mention fields.

High speed multiplication is desired in real-time operations and image processing applications. Various multiplier architectures have been developed using various algorithms such as Booth, array multipliers and Wallace tree. All the aforesaid algorithms use the basic conventional method of multiplication.

Vedic mathematics provides an innovative method of multiplication. Vedic multiplication reduces computation time by parallel generation of intermediate Urdhviate products.

Multiplier designed using Urdhva-tiryakbyham sutra of Vedic mathematics is faster than array multiplier and Booth multiplier architecture and is very efficient in silicon area per speed [3, 4, 5].

Another multiplier using Nikhilam sutra of Vedic mathematics shows similar results when compared to the conventional multipliers [6]. Alternative way of multiplication by Urdhva tiryakbhyam Sutra 3. Dhvanjanka sutra is used in RSA encryption and decryption algorithm. RSA implemented using the overlay hierarchical multiplier architecture and division architecture using Dhvajanka sutra of Vedic mathematics reduces computation time and reduces delay greatly as compared to the RSA implemented using traditional multipliers and division algorithms [8, 9].

Kulkarni analyses and compares the Implementation of Discrete Fourier Transform algorithm by existing and by Vedic mathematics techniques [10]. He suggested that architectural level changes in the entire computation system to accommodate the Vedic Mathematics method increases the overall efficiency of DFT procedure. FFT is widely used in wireless communication imaging etc. Vedic mathematics is an efficient method of multiplication.

Due to the complexity of the operations that needs to be performed nowadays by the processor, the demand for sharing the load by many special purpose processors is increased. Use of Vedic mathematics for multiplication strikes a difference in actual process and hence www. Anvesh kumar used Urdhva tiryakbhyam Sutra of Vedic mathematics to build a power efficient multiplier in the coprocessor [14].

The advantages of Vedic multipliers are increase in speed, decrease in delay, decrease in power consumption and decrease in area occupancy. It is stated that this Vedic coprocessor is more efficient than the conventional one.

The major time consuming arithmetic operations operation in ECC are point additions and doubling as exponentiation operations like square, cube and fourth power occur in these operations. Thapliyal et. A considerable input in the point addition and doubling has been observed when implemented using proposed techniques for exponentiation. Performance Analyses of Vedic Algorithms Various parameters are recommended by researchers to evaluate the performance of Vedic Maths algorithm.

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Researchers suggested many parameters few of them are: Time, Delay, Power and Number of slices. The comparison of Delay ns factor for multiplication implemented in different algorithms between Conventional and Vedic way is shown in Table 1 [15]. Conclusion Vedic mathematics formulae can be used in various algorithms in different computer applications. Various parameters are considered for comparisons of different algorithms. It is concluded that the computer architectures designed using Vedic mathematics are proved to better the conventional architecture in terms of computation speed, power utilisation and silicon area.

Various algorithm based on Vedic maths proved to have faster speed, less power and lesser area. The results obtained are also verified on various FPGAs. Further improvement can be done by reducing the delay caused by propagation of the carry generated from the intermediate products in the multipliers. Thapliyal and M.

Kishore Kumar, A. Tamil Chelvan, S. March-April Khairnar, Ms. Sheetal Kapade, Mr.

Circuits and systems, pp. Download pdf. Remember me on this computer. We can thus avoid multiplication by big digits i. Anurupya and Paravartya will be more suitable. We can take which is one-fourth of or 84 which is one-eighth of it or. The division with as Divisor works out as follows: A few more examples are given below.

The other x must therefore be the product of the x in the lower row and the absolute term in the upper row. The following examples will explain and illustrate i t: This means that the 53 will remain as the Remainder.

But we have 6x in the dividend. This means that we have to get 9x2 more. This must result from the multiplication of x by 9x.

And i x3 divided by x gives us x2 which is therefore the first term of the quotient.

## Vedic Mathematics

But there is no further term left in the Dividend. This can only come in by the multiplication of x by This is the third term of the quotient.

We have therefore to get an additional 53 from somewhere. Hence the second term of the divisor must be 9x. We must therefore get an additional 24x. V and VI relating to Division.

All these considerations arising from our detailedin comparative-study of a large number of examples add up. This astounding method we shall. Formula applicable There And the answer is: And the question therefore naturally— nay. There is a lot of strikingly good material in the Vedic Sutras on this subject too.

And the actual working out thereof is as follows: When the coefficient of x 2 is 1. We do not. And the second factor is obtained by dividing the first coefficient of the Quadratic by the first coefficient of the factor.

In respect. The former has been explained already in connection with the use of multiples and sub-multiples. A Thus we say: X coefficient of that factor. The following additional examples will be found useful: Conjugate Hyperbolas..

This sub-Sutra has actually been used already in the chapters on division. N ote: For example: Bi-quadratics etc. It will be found useful in the factorisation of cubics.

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Sutra just explained and another sub-Sutra which consists of only one compound word. This is obviously a case in which the ratios of the coefficients of the various powers of the various letters are difficult to find o u t.

And that gives us the real factois of the given long expression. The procedure is an argumentative one and is as follows: The procedure is as follows: The 4 Lopana—Sthdpana9 sub-Sutra. That would not. By eliminating two letters at a time. The following exceptions to this rule should be noted: But x is to be found in all the terms ; and there is no means for deciding the proper combinations.

In this case, therefore, x too may be eliminated ; and y and z retained. By so doing, we have: Here too, we can eliminate two letters at a time and thus keep only one letter and the independent term, each time. By Simple Argumentation e. We have already seen how, when a polynomial is divided by a Binomial, a Trinomial etc. From this it follows that, if, in this process, the remainder is found to be zero, it means that the given dividend is divisible by the given divisor, i.

And this means that, if, by some such method, we are able to find out a certain factor of a given expression, the remaining factor or the product of all the remaining factors can be obtained by simple division of the expression in question by the factor already found out by some method of division.

Applying this principle to the case of a cubic, we may say that, if, by the Remainder Theorem or otherwise, we know one Binomial factor of a cubic, simple division by that factor will suffice to enable us to find out the Quadratic which is the product of the remaining two binomial factors. And as the first and last digits thereof are already known to be 1 and 6, their total is 7.

This is a very simple and easy but absolutely certain and effective process. In other words, x — is a factor. But their total should be 0 the coefficient of x 2. So we must reject the 1, 1, 6 group and accept the 1, 2, 3 group. And ti is 48 whose factors are, 1, 2, 3, 4, 6,8 12, 16, 24 and Possible factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and But the sum of the coefficients in each factor must be a factor of the total S0. Now, the only possible numbers here which when added, total —2 are —3, —4 and 5.

Now, test for and verify x —3. Then, argue as in the first method. And the only combination which gives us the total —2, is —1, 2 and —3. Test and verify for —5. And put down the answer. Now test for and verify And that again can be factorised with the aid of the former. The first is by means of factorisation which is not always easy ; and the second is by a process of continuous division like the method used in the G. The latter is a mechanical process and can therefore be applied in all cases.

But it is rather too mechanical and, consequently, long and cumbrous. The Vedic method provides a third method which is applicable to all cases and is, at the same time, free from this disadvantage.

A concrete example will elucidate the process: Let Ej and E2 be the two expressions. The chart is as follows: The Algebraical principle or Proof hereof is as follows: A few more illustrative examples may be seen below: The H.

Multiply it by x and take it over to the right for subtraction. But how should one know this beforehand and start monkeying or experimenting with it?

Thej H. And the beauty of it is that the H. In order to solve such equations. A few examples of this kind are cited hereunder.

## Krsna Tlrtha Maharaj

The student has to perform hundreds of such transposttion-operations in the course of his work. The second common type is one in which each side the L. The usual method is to work out the two multiplications and do the transpovsitions and say: As examples.

Third General Type The third type is one which may be put into the general form. Fourth General Type The fourth type is of the form: And this method can be extended to any number of terms on the same lines as explained above. As already explained in a previous context. But there are. We begin this section with an exposition of several special types of equations which can be solved practically at sightwith the aid of a beautiful special Sutra which reads: On the contrary.

The mere fact that x occurs as a common factor in all the-terms on both sides [or on the L. This is practically axiomatic. In this sense. T h ir d M e a n in g a n d A p p l ic a t io n 4 Samuccaya thirdly means the sum of the Denominators of two fiactions having the same numerical numerator.

Removing the numerical factor.

None need. The two cancelling out.

But there are other cases where the coefficients of x2 are not the same on the two sides. Let us take a concrete example and suppose we have to solve the equation? In the first case. But it does not matter. At sight. It is as simple and as easy as the fourth application.

In the two instances given above. The Vedic Sutra. And that is all there is to it! A few more instances may be noted: M ed iu m D isguises The above were cases of thin disguises. We now turn to cases of disguises of medium thickness 1 x —2. All this argumentation cun of course. And that test is quite simple and easy: There must therefore be some valid and convincing test whereby we can satisfy ourselves beforehand on this point and.

And this too can be done mentally. By simple division. By either method. And x —6 is the factor under the cube on R. Taking away the numerical factor. The Vedic mathematicians. Vedic one-line mental answer is: Cancelling common terms out. And this gives us the required clue to the particular characteristic which characterises this type of equations.

N1 Dx and D2 Binomials? And this too gives us the same answer as before. The Vedic formula. And here too. On actual cross-multiplication and expansion etc. An instance in point is given below: The student should not. In the fourth case. And we get the same answer as before.

But it is not a sufficient condition by itself for the applicability of the present formula. This really comes in as a corollary-consequence of the A. And this is in confiormity with the lack of the basic condition in question i.

This gives us the assurance that. In the example actually now before us.

This section may. But what about the x2 coefficients? For them too to vanish. The Algebraical Explanation for this type of equations is: We now proceed to deal with certain types of cases which do not seem to be of this kind but aie really so. And there is no quadratic equation left for us to solve herein P roof: The x 2 coefficients are: All that we have to do is to re-arrange the terms in such a manner as to unmask the masked terms.

The first type: The first variety is one in which a number of terms on the left hand side is equated to a single term on the right hand side. As we mean to merge the R.. And the process is complete.. S is to be merged. So the resultant new equation after the merger now reads: A few more examples of this sort may be noted: A few illustrations will make this clear: A few more illustrations of this type are given below: YES 2 In these examples. For instance: In such cases. T h e Sutra applies and can be applied immediately without bothering about the L.

S of the same equation. A few more illustrations will be found helpful: This will be explained later. This equation can be solved in several ways all of them very simple and easy: N is also 24 The Sutra applies.

In the final derived equation. The Sutra applies. The student may. By Pardvartya devisioD twice over. The Vedic method by the Pardvartya Rule enables us to give the answer immediately by mere mental Arithmetic. And this. But even here. And this gives us our Numerator. And the Sutra says that. The Algebraical Proof is this: This gives us two simple equations in y. An example will make the meaning and the application clear: If one is in ratio.

And a repetition of the same.

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T h i s rule is also capable of infinite extension and may be extended to any number of unknown quantities. And the whole work can be done mentally. And we can say. As this is simple and easy to remember and to apply. A few of them are shown below. There are other types of miscellaneous linear equations which can be treated by the Vedic Sutras.

The Sutra. Let d be the common difference. C and D are in AP.

## Vedic Mathematics - Ancient Fast Mental Math (Discoveries, History, and Sutras)

Another Algebraical proof. Vedic Mathematics But the Sunyam Samuccaye Sutra does not apply beacnse the number of factors in the original shape is 2 on the L. B E A few more examples may be taken: We therefore deal with this special type here.

The case is exactly like the one above. And this proves the proposition in question.

## Vedic Mathematics

A few more illustrations are taken..Ginitasamucchayah 2. Three Proofs of Fermat's Last Theorem. His inspiring words are like fragrant flowers offered at the feet of the ancient Vedic R6is whose spiritual lineage was revealed in the late Sankaracarya Sri Bharatl Krsna Tlrtha. We believe this paper was a reaction by some in the academic community to certain elements of the Hindu community trying to use Vedic Mathematics to promote Hinduism by teaching Vedic Mathematics in schools.

In this method, in the above example, 1 is the first multi plicand and its product with multiplier 2 is 2 which in this special process becomes the second multiplicand.

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.

Thapliyal and M. To solve the aptitude questions faster and in under a minute, we must practice questions and must know all types of shortcuts which can help. The numbers taken can be either less or more than the base considered.

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