72 - Special and General Methods


ISSUE No. 72

A warm welcome to our new subscribers.
Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given. If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.


This issue's article is by your editor, Kenneth Williams.



In the Vedic system we have special methods as well as general methods. And some of these special methods are so spectacular that they get a lot of publicity, and consequently Vedic mathematics is getting a reputation for being just 'tricks'. The method of multiplying numbers near a base, like 100, and the method of squaring numbers that end in 5 are examples of this. But it is a misconception to think Vedic maths is just tricks, because the Vedic system is a complete system of mathematics.

In Vedic Maths we always have a general method for multiplication, division, square roots etc. But the Vedic system is enriched by many special methods. These allow, in some cases, extremely difficult problems to be solved with great ease. It is a real delight to see a complex equation solved instantly because it is recognized as coming under one of the special methods, and small children can do this sort of thing too.

Actually special methods are in common use. For example asked to find 77 x 10 the conventional system does not treat this as long multiplication, but uses a special technique, or trick, that you can just append a zero to the 77 to get 770.

And special methods are in common use in our thinking too: to solve a problem in everyday life we usually go for the most efficient solution. Every problem is solved uniquely on its own merits. The carpenter does not use a chisel for every job but selects the tool appropriate to the task he has to do. Why not take the same approach to maths? It's clumsy and inappropriate to use just one method of multiplication if there is a method especially suited to the problem in hand.

Having just one general method also means teaching becomes rigid: the calculation has to be done in one way and variations by children are even sometimes pronounced 'wrong' just because they're different. Children, especially the more creative types, rebel at this rigidity as they feel constrained. And it does not have to be like that; there is tremendous scope in mathematics for variation, experimentation and innovation. In this way maths becomes more like a game.

This is where the Vedic system promotes creativity, as the variety of methods encourages the children to find their own solution and even invent their own methods. Once children realize that they are being encouraged to be inventive they generally respond with enthusiasm.

In this way Vedic Math appeals to the artistic types as well as to the more analytic types. And children can absorb as many of the special methods as they wish. They need to know the general methods but can choose which special methods they want to know.

Suppose, for example, you are faced with the product 29 x 31. You can of course use the general method for finding the product of two 2-figure numbers. But you may notice that the number 30 is in the middle between 29 and 31. And so the answer may be the same as 30 x 30 or close to it.

But 30 x 30 is 900 which is clearly not the answer. In fact the answer is 899, 1 less than 900.

Similarly, you can find 39 x 41 by finding 40 x 40 and subtracting 1.
So 39 x 41 is 1600 - 1 = 1599.

This makes this kind of product very easy to find and the method can be extended to other products like 37 x 43 (or any product where the average of the numbers is easy to square). Such investigations can lead to the discovery of the formula for the difference of two squares.

These special methods are not confined to elementary mathematics, and at a higher level the saving in time and effort in using them can be far greater. Tirthaji himself gives many examples of complex equations which are special types or which can be easily manipulated into the form of a special type.

To claim that students should not be taught special methods because it might confuse them is a false economy, though special methods taught in a rigid way may lead to this. The aim of education is to draw the knowledge and creativity out of the pupil and this is achieved by getting them involved, enlivened and stimulated by the subject.

The new area of research called Cognitive Load Theory aims to measure the mental load involved in some mental activity: say multiplying two numbers.

Knowing a special method involves a load on the mind, because you have to know the special characteristics which indicate that that method can be applied. But it can also save time and lessen the load that would otherwise be involved.

Although the creative aspect mentioned earlier, and the fun involved, cannot be quantified by this theory, the special Vedic methods should be examined in terms of cognitive load.

So if you are demonstrating some of the amazing Vedic methods please also mention that these are just a part of a complete system of maths called Vedic Mathematics.





You can listen to an audio recording of Sri Bharati Krsna Tirthaji answering a question from British historian Arnold Toynbee in 1958 here:



High Speed Reconfigurable FFT Design by Vedic Mathematics.
By Ashish Raman, Anvesh Kumar and R.K.Sarin

Abstract-The Fast Fourier Transform (FFT) is a computationally intensive digital signal processing (DSP) function widely used in applications such as imaging, software-defined radio, wireless communication, instrumentation. In this paper, a reconfigurable FFT design using Vedic multiplier with high speed and small area is presented. Urdhava Triyakbhyam algorithm of ancient Indian Vedic Mathematics is utilized to improve its efficiency. In the proposed architecture, the 4x4 bit multiplication operation is fragmented reconfigurable FFT modules. The 4x4 multiplication modules are implemented using small 2x2bit multipliers. Reconfigurability at run time is provided for attaining power saving. The reconfigurable FFT has been designed, optimized and implemented on an FPGA based system. This reconfigurable FFT is having the high speed and small area as compared to the conventional FFT.

This is published in the Journal of Computer Science and Engineering, Volume 1, Issue 1 May 2010. You can view the full article here:


A parent is looking for tuition in Thailand or the Philippines to learn Vedic Maths in order to teach her children.

If you can help please contact Ms Huynh Thi Bac at


We are looking for someone, possibly a post-graduate student, who can go through and check the last four chapters of the book "Vertically and Crosswise".
These are on Functions of Polynomials & Bipolynomials, the Solution of Linear and Non-Linear Differential, Integral and Integro-Differential Equations and The Solution of Linear and Non-Linear Partial Differential Equations.
Payment is available. If you are interested please contact


A new YouTube video on Vedic Mathematics can be viewed at:

This shows the general multiplication method: how it's easy to explain, how it can be done from right to left or left to right, how it enables the product of any two numbers to be found in one line, how it's reversible so that divisions can be carried out in one line and how it enables easy products of algebraic expressions too, which is also reversible.


Your comments about this Newsletter are invited.
If you would like to send us details about your work or submit an article or details about a course/talk etc. for inclusion, please let us know on

Previous issues of this Newsletter can be copied from the Web Site: www.vedicmaths.org
Please pass a copy of this Newsletter on to anyone you think may be interested.

Editor: Kenneth Williams

Visit the Vedic Mathematics web site at: http://www.vedicmaths.org

3rd January 2011


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