ISSUE No. 18

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.

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This issue's article:

This fascinating article was sent by Luigi Di Martino and shows how the Vedic Square, featured in other newsletters (numbers 7 and 16), arises from divisions as well as from multiplication.

The Vedic Matrix/Square is a nine by nine square array of numbers formed by taking a multiplication table (up to nine times nine) and replacing each number by its digit sum. The digit sum is found by adding the digits in a number and adding again if necessary:
42 becomes 6 and
56 becomes 11 which becomes 2.
So the first row of the Vedic Square consists of 1,2,3,4,5,6,7,8,9 and the second row is 2,4,6,8,1,3,5,7,9 and so on.

Thus the Vedic Square is constructed by multiplying each of the numbers 1 to 9 by each of the numbers 1 to 9 and applying the digit sum. Luigi does a similar thing but divides instead multiplying.

## 9 BY 9 DIVISION TABLE

1/1 = 1                2/1 = 2                3/1 = 3
1/2 = 0.5             2/2 = 1                3/2 = 1.5
1/3 = 0.3333       2/3 = 0.6666       3/3 = 1
1/4 = 0.25           2/4 = 0.5             3/4 = 0.75
1/5 = 0.2             2/5 = 0.4             3/5 = 0.6
1/6 = 0.1666       2/6 = 0.3333       3/6 = 0.5
1/7 = 0.142857   2/7 = 0.285714   3/7 = 0.428571
1/8 = 0.125         2/8 = 0.25           3/8 = 0.375
1/9 = 0.1111       2/9 = 0.2222       3/9 = 0.3333

4/1 = 4                5/1 = 5                6/1 = 6
4/2 = 2                5/2 = 2.5             6/2 = 3
4/3 = 1.3333       5/3 = 1.6666       6/3 = 2
4/4 = 1                5/4 = 1.25           6/4 = 1.5
4/5 = 0.8             5/5 = 1                6/5 = 1.2
4/6 = 0.6666       5/6 = 0.8333       6/6 = 1
4/7 = 0.571428   5/7 = 0.714285   6/7 = 0.857142
4/8 = 0.5             5/8 = 0.625         6/8 = 0.75
4/9 = 0.4444       5/9 = 0.5555       6/9 = 0.6666

7/1 = 7                8/1 = 8                9/1 = 9
7/2 = 3.5             8/2 = 4                9/2 = 4.5
7/3 = 2.3333       8/3 = 2.6666       9/3 = 3
7/4 = 1.75           8/4 = 2                9/4 = 2.25
7/5 = 1.4             8/5 = 1.6             9/5 = 1.8
7/6 = 1.1666       8/6 = 1.3333       9/6 = 1.5
7/7 = 1                8/7 = 1.142857   9/7 = 1.285714
7/8 = 0.875         8/8 = 1                9/8 = 1.125
7/9 = 0.7777       8/9 = 0.8888       9/9 = 0.9999

Results

Dividing by 1 gives the first number sequence of the 'Vedic' Square - 1 2 3 4 5 6 7 8 9

Dividing by 2 gives fifth number sequence - 5 1 6 2 7 3 8 4 9 (For 3/2 = 1.5 we add the digits: 1+5=6. Similarly for the other answers consisting of more than one digit; i.e. we take their digit sum.)

Dividing by 3 gives a sequence which is a recurring total .3333. Yet you will see that numbers divided by 9 possess recurring totals which hide all the 9 number sequences of the Vedic Square.

Dividing by 4 gives the 7 number sequence - 7 5 3 1 8 6 4 2 9

Dividing by 5 gives the reverse of the 7 sequence instead, the number 2 sequence - 2 4 6 8 1 3 5 7 9

Dividing by 6 gives the second recurring total, up in increments of .1666. This total is half the .3333 when numbers are divided by 3.

Dividing by 7 gives a very interesting result. This is the first of a series of 'CONSTANTS' which manifest through division. The sevens go up in increments of 0 .142857. From here on any number divided by seven will produce this sequence in different orders. Dividing by seven creates a loop of six overall divisions, and after that the sixth returns to the first. These 'constants' keep returning as we divide by higher and higher numbers. Dividing by numbers higher than 9 will highlight this so there is much profit in extending this 9 by 9 division table.

Dividing by 8 gives the reverse number sequence as dividing by 1 - 8 7 6 5 4 3 2 1 9

Dividing by 9 opens up all the number sequences. Firstly, dividing numbers in sequence by 9 gives increments of 0.1111. Yet if we add the figures together we will be exposing a hidden number sequence. Lets take the 0.1111 recurring total. We start with 1. We then add on the next 1 and therefore we now have 2. We add on the next number in the recurring total, another 1, and it makes 3. This will eventually expose the 1st number sequence of the Vedic Square. Similarly, with the 0.2222 recurring total we get the 2 4 6 8 1 3 5 7 9 number sequence by adding the first figure, the first two figures and so on.

0.111 is the 1 2 3 4 5 6 7 8 9 number sequence in disguise
0.222 is the 2 4 6 8 1 3 5 7 9 number sequence in disguise etc.
0.333          3 6 9 3 6 9 3 6 9
0.444          4 8 3 7 2 6 1 5 9
0.555          5 1 6 2 7 3 8 4 9
0.666          6 3 9 6 3 9 6 3 9
0.777          7 5 3 1 8 6 4 2 9
0.888          8 7 6 5 4 3 2 1 9
0.999          9 9 9 9 9 9 9 9 9

Other divisions

Dividing by 10 gives the same number sequence as dividing by 1. But dividing by 20 will not give the same, it will give the 5 1 6 2 7 3 8 4 9 sequence, which is same as dividing by 2. One would think that dividing by 19 would give the number sequence 1 as well but in fact dividing by 19 gives a very long set of numbers. This 17 digit sum is a CONSTANT and it adds up to 81, which breaks down to 9. As any number is divided by 19 this 17 digit constant appears continually in different orders.

Dividing by 11 gives another unique structure which has some relationship with the number 9. Firstly it resembles the inversions of a Major scale. It also equates, by implications the number 9 with number 0. Check this out for yourself and see if you can find more musical connotations within these 9 number sequences. Equate each number within the Vedic Square with a note from the C Major scale - C D E F G A B C - give each note a number (make D also equal 9 as well as 2) and uncover a number/note grid. These hybrid scales can sound very Modal and can open up some very nice sounding accompaniment chords for Modal playing for example. These are exposed if you harmonise the resulting number scales.

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## NEWS

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WORKSHOP IN VICTORIA, AUSTRALIA

The Annual conference of Mathematics Association of Victoria, Australia is on 6 and 7 December 2001. There are around 2000 teachers attending the conference. A workshop given by Madhavi Tembe will be on both days.
Contact details are E-mail: Website: http://www.mav.vic.edu.au
Telephone number: 61 3 9380 2399, Fax: 61 3 9389 0399

VEDIC MATHEMATICS AT A SATURDAY MORNING SCHOOL

On Saturday 21st July Andrew Nicholas showed three groups of youngsters some mental mathematics and geometry, and left an appetite for more. The 11-13 year olds responded quite well to geometry, but the 8-9 year olds found it more challenging - perhaps because they had not done any at day school. The 6-7 year olds were given simple examples in arithmetic, to which they responded enthusiastically.

Vedic Mathematician wanted (The Eagle Education Project) The school where Andrew taught is based at Southgate, north London. It aims to ensure that the children enjoy learning and that they really do learn something. Use is made of some of the innovative teaching methods developed in recent years. They would like Vedic Mathematics to be taught there, on Saturday mornings. If anyone is willing and able to do this (it is quite well paid) contact Kenneth Williams at , giving some details about yourself. VEDIC

MATHS LESSONS IN MUMBAI, INDIA

We sometimes get inquiries from people wanting Vedic Maths lessons so we are pleased to hear about Dr Abhijit Das who teaches Vedic Maths in Mumbai. He can teach either individuals or groups, preferred age range 8+ to adults. Dr Das is a surgeon and a member of MENSA. He can be contacted by email at:

AGAINST VEDIC MATHEMATICS

A statement was issued on 13th August, with names of over a hundred scientists and academicians, mostly in India, against the inclusion of Vedic mathematics and Vedic astrology in NCERT and UGC curricula in India. It seems the NCERT and UGC offer funds to institutions that teach courses in certain subjects. The Times of India, New Delhi, printed a short article the following day. We have seen two versions of this statement, sent by readers of this newsletter, both of which are very inaccurate and emotionally charged. From the text of this statement it would appear that its author had given no more than a cursory look at the original work by Sri Bharati Krsna Tirthaji and was not aware of the research and educational developments that have taken place since this was written.

VEDIC SQUARE

Sue Clear in Oxford, England has sent us some Vedic Squares in different bases (2 to 10). This is something interesting to explore.

GOLDBACH CONJECTURE

If you are wondering what became of the proof of this by Dr Kapoor, it is still undergoing lively discussion. We will keep you informed.

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CORRESPONDENCE

EMAIL: I found the 7 tutorials on Vedic Maths on Internet in 2000. I used that with some of my students then. This year I spent one week with each of my classes and taught them these methods of multiplying and dividing. For the first time students were eager to do maths and wanted more of it.

EMAIL: I came to your site and got very interested in vedic maths, would like to find out address's in Bombay where I can learn vedic maths.

EMAIL: I want to subscribe to the newsletter of Vedic Math. I am basically a software engineer in Hyderabad, India. I will be using the mathematics a lot in my job. In order to improve my math skills, I regularly use vedic math techniques for calculations.

EMAIL: Thank you for getting back. I cannot express the joy that came over me when I decided to do some of the tutorials on the Vedic Maths web site! I can see that I am going to get quite involved in these structures or sutras. I will be hoping to get more time to study the subject a little more in depth. I have spent the last week plotting out a 24 by 24 divisions table! In doing so I have spotted what happens to the 9 number sequences. This is probably another Vedic technique and I am going to see the same information one day through one of your newsletters! I will be happy to pass the results on to you in case it has been overlooked.
I believe that Nature is like a good computer program that has been exquisitely written in laws that defy us most of the time. Being able to follow the path that 9 number sequences take me to is one way of deciphering the programming as I am sure that these are the building blocks that more and more structures come to exist.

EMAIL: I am regularly going through the articles. Thanks a lot. I was fortunate to use the book by Swamiji himself, however it was possible only for a fortnight since it was borrowed from a friends library. It is very unfortunate to understand from the major book stores that this book is out of print. The people who want to learn this fast and accurate method of mental calculations cant buy this book. Books that are printed in U.K. are very expensive. Is any publisher making any attempts to bring down the costs so that people like me who are sincerely interested in learning can afford to buy them? Also is it possible to have more sums solved in your regular articles?

REPLY: Swamiji's book is available and is not out of print. The publisher is Motilal Banarsidass (details below). The UK books are expensive as you say. This is because we print only when ordered until the books are properly published. Motilal Banarsidass are going to publish them beginning with the Cosmic Computer course. These should then be available at low prices. I am glad you find the articles useful. More sums is a good idea but the newsletter is time consuming to produce. Perhaps you would like to contribute something?

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If you would like to send us details about your work or submit an article for inclusion please let us know on

Articles in previous issues of this Newsletter can be copied from the web site - www.vedicmaths.org:
Issue 1: An Introduction
Issue 2: "So What's so Special about Vedic Mathematics?"
Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius
Issue 4: The Vedic Numerical Code
Issue 5: "Mathematics of the Millennium"- Seminar in Singapore
Issue 6: The Sutras of Vedic Mathematics
Issue 7: The Vedic Square
Issue 8: The Nine Point Circle
Issue 9: The Vedic Triangle
Issue 10: Proof of Goldbach's Conjecture
Issue 11: Is Knowledge Essentially Simple?
Issue 12: Left to Right or Right to Left?
Issue 13: The Vinculum and other Devices
Issue 14: 1,2,3,4: Pythagoras and the Cosmology of Number
Issue 15: A Descriptive Preparatory Note on the Astounding Wonders of Ancient Indian Vedic
Issue 16: Vedic Matrix Issue
Issue 17: Vedic Sources of Vedic Mathematics Mathematics

To subscribe or unsubscribe to this Newsletter simply send an email to that effect to
Please pass a copy of this Newsletter on (unedited) to anyone you think may be interested.
Editor: Kenneth Williams

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

Email

4th September 2001