65 - The Living Mathematics of Nature


ISSUE No. 65

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 lead article was published by the Times of India on May 30, 2009. The author, Mr K.S. Raman, is a Vedic Mathematics practitioner at Nagpur who conducts classes for school going children and students appearing for competitive examinations including CAT.


Vedic Mathematics has originated from the Indian Vedas. Vedic Mathematics is not only an introduction to ancient Indian civilization but also takes us back to many millennia of India's mathematical heritage. Rooted in the ancient Vedic sources which heralded the dawn of human history and illumined by their erudite exegeses, India's intellectual, scientific and aesthetic vitality blossomed and triumphed not only in philosophy, physics, ecology and performing arts but also in geometry, algebra and arithmetic. Indian mathematicians gave the world the numerals now in universal use. The crowning glory of Indian mathematics was the invention of 'Zero' and the introduction of the decimal notation without which mathematics as a scientific discipline could not have made much headway. It is noteworthy that the ancient Greeks and Romans did not have the decimal notation and therefore, did not make much progress in the numerical sciences. The Arabs first learnt the decimal notation from Indians and introduced it into Europe. The renowned Arab scholar Alberuni, who was born in 973 AD and traveled to India, testified that the Indian attainments in mathematics were unrivalled and unsurpassed. In keeping with that ingrained tradition of mathematics in India, Ramanujam, "the man who knew infinity", the genius who was one of the greatest mathematicians of our time and the mystic for whom " a mathematical equation had a meaning because it expressed a thought of God", blazed new mathematical trails in Cambridge University in the second decade of the 20th century even though he did not himself possess a university degree.

Vedic Mathematics is a new and unique system based on simple rules and principles that enable mathematical problems of all kinds to be solved easily and efficiently. The methods and techniques are based on the pioneering work of the late Bharati Krishna Tirthaji, the Shankaracharya of Puri, who established the system from the study of ancient Vedic texts coupled with a profound insight into the natural processes of mathematical reasoning. The Indian Vedas deal with many subjects but the texts are frequently difficult to understand. They are concerned with the spiritual and secular aspects of life because, in those times, no essential difference was perceived between the two. The Shankaracharya of Puri made great efforts to dig out the system of mathematics from these texts and came up with this unique system of mathematics.

Vedic Mathematics was traditionally taught orally through aphorisms or Sutras. A Sutra is a thread of knowledge, a theorem, a ground norm, a repository of proof. It is formulated as a proposition to encapsulate a rule or a principle. A single Sutra would generally encompass a wide and varied range of particular applications and may be likened to a programmed chip of our computer age. These aphorisms of Vedic Mathematics have much in common with aphorisms which are contained in Panini's Ashtadhyayi, that grand edifice of Sanskrit grammar. Both Vedic Mathematics and Sanskrit grammar are built on the foundations of rigorous logic and on a deep understanding of how the human mind works. The methodology of Vedic Mathematics and Sanskrit grammar help to hone the human intellect and to guide and groom the human mind into modes of logical reasoning.

Experience of teaching Vedic Mathematics to children has shown that a high degree of mathematical ability can be attained from an early age while the subject is enjoyed for its simplicity and ease. Many of the methods are developed further at a later stage. An important characteristic is that, although there are general methods for calculations, there are also methods for particular types of calculations. For example, specifically in multiplying and dividing numbers close to a base of ten, a hundred, a thousand, etc. Where such particular methods are introduced at an early stage, it is because they relate to more general aspects of the system at a later stage or are simply very quick and easy ways to obtain answers.

The current methods of calculating which most schools have adopted are "blanket" methods. For example, with division, only one method is taught and actually used by the children. Although it will suffice in all the cases it may often be difficult to use. The Vedic system teaches 3 basic algorithms for division that are applied to meet the particular need in hand although each could be used for any division sum. The principle is that, if a particular sum can be done by an easier method, then that method should be used. Of course, with children, some mastery of the different methods must be accomplished before this more creative approach can be adopted.
In Vedic Mathematics, there basically are two guiding maxims. The first is that the whole number system is made of 9 numbers and a zero, and that these numbers represent the nine 'Elements' as described in the ancient scriptural texts of India. The 2nd is that the whole of mathematics is governed by the 16 Sutras, or short formula-like aphorisms, which are both subjective and objective in character. They are objective in that they may be applied to solve everyday problems. The subjective part of the Sutra is that it may also describe the way the human minds naturally works. The whole emphasis of the system is on the process and movement taking place in the mind at the time that a problem is being solved. The effect of this is to bring attention into the present moment. The main emphasis at the early stages is to develop numeracy, which is the most important aspect of mathematics.

Vedic Mathematics appears, at first, to have a magical quality. When the methods are understood, particularly in relation to one another, then it is unified mathematics. In the Vedic mathematics system, the very first step is to recognize the pattern of the problem and pick up the most appropriate and efficient Vedic algorithm to solve it. Further, at each subsequent step, we recognize the pattern and complete the task by using the appropriate superfast mental technique, because in Vedic Maths we have multiple choices available at each step of working. Needless to say, there are crosschecking methods also available at different levels and finally a verification method to ensure that the answer arrived at is correct or not. As such, by a regular practice of the most natural mental procedures of the Vedic Maths system, the holistic development of the human
brain takes place. In a nutshell, we can say that Vedic Maths provides the cosmic software for the cosmic computer (the human brain). The use of this Divine System of Mathematics automatically activates the most powerful facet of human personality - the intuitive faculty, which unfortunately remains undeveloped in most of the students due to the present curriculum of mathematics education being imparted in schools and colleges.

To quote Dr. L.M. Singhvi, Former High Commissioner for India in the UK and a great patron of Vedic Mathematics, " I do not wish to claim for Vedic Mathematics as we know today the status of a discipline which has perfect answers to every problem. I do question those who mindlessly deride the very idea and nomenclature of Vedic Mathematics and regard it as an anathema. They are obviously affiliated to ideological prejudices and their ignorance is matched only by their arrogance. Their mindset was bequeathed to them by Lord Macaulay who knew next to nothing of India's scientific and cultural heritage. They suffer from an incurable lack of self-esteem coupled with an irrational and obscurantist unwillingness to celebrate the glory of Indian achievements in the disciplines of mathematics, astronomy, architecture, town planning, physics, philosophy, metaphysics, metallurgy, botany and medicine. Let us reinstate reasons as well as intuition and let us give a fair chance to the valuable insights of the past. Let us use that precious knowledge as a building block. To the detractors of Vedic Mathematics I would like to make a plea for sanity, objectivity and balance. They do not have to abuse or disown the past in order to praise the present."

It is difficult to appreciate the full benefits of Vedic Mathematics unless one gets immersed in the techniques, leaving behind all previous paradigms and prejudices about mathematics. We can see for ourselves at Nagpur how numerous average children, who have undergone this system with us coupled with their dedication and hard work, have made it to the merit list of various Boards and succeeded in competitive examinations in recent years. And that number will swell every year with more child geniuses waiting to prove their worth in the coming years. That is the positive benefit of the Vedic Mathematics and just cannot be ignored. So let us all embark upon a journey of producing child geniuses of which we can be proud of instead of talking negative about this pure and positive science. Let us impart this knowledge to the future generation in a bid to make strong individuals and the strongest country in the world by the year 2020. Let us start today patronizing this great science which children learn with smiles on their faces and joy in their hearts.

It is surprising to note that many countries in the world have already started accepting this system. Our neighbours, Malaysia, Indonesia, Singapore and Dubai have full-fledged centers. The Bhartiya Vidya Bhavan at Manchester, London conducts regular classes in Vedic Mathematics. Australia, Doha (Qatar) and Muscat are becoming important centers of learning of Vedic Mathematics apart from Germany, The Netherlands, the UK, the USA, etc. It is also reported that the Japanese are going to send some of their people to India to learn Vedic Mathematics. What are we waiting for? Do we need the West always to tell us what is good for us? This we should not allow and start propagating this positive science in India and Nagpur in particular, which is fast emerging as an important educational hub.

Mr Raman can be contacted on mobile 09325339383 or at





This unusual and well-explained method of multiplying by 9 is from R. Amirthaa. (VII Std, Indian School Muscat).

423 X 9 = ?

( 1 )
x y z
4 2 3 X 9
a b c
Write the Number like this and write the Compliment of each digit of the Multiplicand from 10 on top as x,y,z. Write the predecessor of each digit of the Multiplicand as a,b,c.
( 2 ) Then your answer is
a, x+b, y+c, z.
( 3 ) You can try to multiply any number of digit by 9 like this.


If you are teaching Vedic Maths or expect to be soon, and would like to join a group within the Academy devoted primarily to the promotion of Vedic Mathematics please send an email to saying you are interested. We will then contact you with details.


An article with the above title was published in The News & Observer, a North Carolina-based newspaper, on August 10th. Apparently Albert Clay in the US has copyrighted a method by which he can multiply any number by any number in a single line. This appears to be the same as the Vedic vertical and crosswise multiplication method.

Here is a link to the article:

"You can't copyright ideas, but you can get the legal rights to the way you explain them" his attorney said. Mr Clay appears to be unaware that this method is very ancient and he should have done some research before laying claim. In fact when Fibonacci wrote his famous book Liber Abaci in 1201, in which the Indian number system was introduced to the west, the vertical and crosswise method was one of those given for multiplying numbers. Gaurav Tekriwal of the Vedic Maths Forum India is organizing a response to this.


I am Sumit Sharma, B.E. IV yr Student (I.T.M., Bhilwara), presenting a method of cubing a no. having 5 as the last digit.

15^3 = [15* (1*2) + (1+2)], 15*5 = (30 + 3), 75 = 3375

45^3 = [45*(4*5) + (4+5)], 45*5 = (900 + 9), 225 = 909, 225 = 90, (9+2), 25 = 91125

195^3 = [195*(19*20) + (19+20)], 195*5 = 74100 + 39, 975 = 74139,975

= 7413, (9+9), 75 = 7414875

So we can say that

(xy)^3 = [xy*x*(x+1) + (2x+1)], xy*5


Phase two of my Tactile Math has taken about ten years to unfold. I finally have a small research team together. Our Undergraduate Research Assistant, Sheila Schneider* has helped me come up with a brilliant idea.
> We are collecting the vibrator-motors from spent Oral-B Pulsar
> toothbrushes to use as vibro-tactile actuators in a limited-edition
> sculpture. We are doing a research programme in Maths education for
> the visually impaired at the University of Illinois at
> Urbana-Champaign. Your spent Pulsar toothbrush might become part of a
> 3-D computer animation for the blind. Please send your old Pulsar
> toothbrush to: Stewart Dickson, Visualization Programmer,
> Beckman Institute - South Facility, Room 12, 2100 S. Goodwin Urbana,
> IL 61801
> Ph: 217-333-3923 Fax: 217-244-1827, email: --
> Thanks! --Stewart

o When a statement in mathematical language is rendered into a three-dimensional sculpture, the abstract statement which generated the form becomes separated from the physical manifestation of the form, itself.

o You have to use a lot of words to describe a mathematical sculpture and to explain its significance. The significance of the form is only self-evident to the previously initiated.

o Physical sculpture via rapid-prototyping is the obvious way to provide access to mathematical, visual computing to the visually impaired, but, there must a more intuitive way to communicate the significance of the physical form via tactile captions.

o There exist a class of mathematical algorithms with reduced cognitive load -- They include the Trachtenberg system and the Hindu Vedic sutras for mental mathematics.

Our goal is to create a series of sculptures which inspire a fascination for mathematics. We are studying sign-language-like hand gestures suggested by the Vedic algorithms which we can convert into tactile glyphs to use in captioning our sculptures. I am initiating the sculpture design with a series of computer-generated animations, after the style of Jim Blinn** which visually mechanises the Vedic algorithms. These animations then directly suggest sculpture and the scheme for captioning.

How do you show time-sequence in a 3D tactile model? Using pager (or disposable toothbrush!) vibrator motors and an electronic sequencer. Research has shown a one-to-one cognitive mapping from visually observed hand gestures to spatially-separated vibro-tactile signals.***

*Sheila is the first-ever legally blind student in sculpture at the College of Fine and Applied Arts at the University of Illinois ar Urbana-Champaign.
**James Blinn was the author of "The Mechanical Universe", "Project
Mathematics!" and the space mission simulations from the NASA Jet Propulsion Laboratory at California Institute of Technology. He was also a star of the SIGGRAPH Electronic Theater during the 1980's and 1990's.
Wired.com: Danger Room What's Next in National Security
DARPA Wants Soldiers to Touch, From 300 Feet Away
* By Noah Shachtman Email Author, * April 23, 2008 | * 8:25 am | *

FIND THE SQUARES - from Neeta Vithalkar

a) 44444^2=
b) 555^2=
c) 99999^2=
d) 66666^2=
now we can observe the repetition of a digit in all these numbers. In such pattern we can use the duplex method to find the square.
a) 44444^2=
· count the 4's
· it comes for 5 times in the numbers
· so now in ans. write down square of 4 that is 16 as the last part of the ans.
· than go on writing table of 16 for 5 times (duplex of the numbers will give us the table of 16)
· than reverse of the table of 16 up to 1
· 16/32/48/64/80/64/48/32/16
· as we know tens digits are carry overs so our ans. is
· 1975269136
b) 555^2=25/50/75/50/25=308025
what if the numbers are
I know ! do you?

Please send your answer to Neeta's question to


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


14th August 2009


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