13 - The Vinculum and other devices


ISSUE No. 13

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.
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:


The Vedic system uses a variety of methods for simplifying calculations. The vinculum is one of these as it allows us to remove some or all digits over five from a calculation so that only 0, 1, 2, 3, 4 and 5 are used.

The vinculum is a horizontal line written over a digit which thereby makes it negative. So 19 could be written as twenty minus one, i.e. 2(-1), where we write (-1) instead one with a bar over it (as we cannot write that in an email). This is quite natural as most people would, for example, add 19 by adding 20 and taking one away.

Similarly 38 would be written as 4(-2), that is 4 followed by a 2 with a bar over it, 98 becomes 10(-2), one hundred take away two, and 283 = 3(-2)3, three hundred, minus twenty, add three.

So we can have numbers which are partly positive and partly negative.

This increases flexibility as it means we have a choice whether or not to use the vinculum and in fact we can convert any number into a variety of vinculum forms using the vinculum device. So 46 for example could also be written as 5(-4), or as 1(-5)(-4). We use the form that is appropriate depending on what we want to do with the number.

In this way 0 and 1, which are particularly easy to work with, occur twice as often. This also means that in a calculation where the vinculum is used the positive and negative numbers tend to cancel each other out so that we can work with smaller numbers, and in fact, because of the flexibility the vinculum allows, we can choose to use forms of numbers that maximise this cancelling. So we have more control over a calculation: if you are finding a sine or cosine for example you can arrange to keep any carry figures to a minimum.

The use of the vinculum is optional though: all the marvellous Vedic methods can be carried out without using the it. But it can also simplify things a lot and so it is certainly worth experimenting with and getting familiar with working with a mixture of positive and negative digits, or even just using it occasionally when it is obviously an advantage.

We can also write numbers in different forms without using the vinculum. 46 for example can be written as 3/16 where the "1" is written as a subscript (and the oblique line is not written), so 3/16 means 30+16. And we can combine this with the vinculum to get yet more forms of the same number.

In division too answers can be expressed in a variety of ways. If you divide 20 by 7 you get 2 remainder 6. But 3 remainder (-1) is also a valid answer and so is 1 remainder 13 and so on.

This element of choice in the Vedic system leads to flexibility and creativity and so is very useful nowadays when these qualities are particularly important for developing the young mind.





Maharishi Ayurveda Products (MAP) sell four Vedic Mathematics books and they have credit card facilities. The Abridged Cosmic Computer book (probably the best introduction to Vedic Mathematics) can be purchased from them for 15 pounds. The other books available are: The Natural Calculator, Discover Vedic Mathematics and Triples. MAP details are:

Tel: +44 1695 51015


We have had an inquiry about a support system for teachers who want to explore Vedic Maths. If you have any ideas about how this could work please let us know. One idea is to have a Bulletin Board on the web site where messages, ideas, teaching materials and methods could be placed.


Clive has now created a Chatroom on the Vedic Maths web site. We are not quite sure how it might be used yet but the link is at the bottom of the home page. You go initially into a Reception area from where you can enter any of five rooms. Clive also intends to create a Bulletin Board and an Address Book on the site.


The weekend newspaper Business Standard in India published an excellent article on Vedic Maths on 11th and 12th November called "How the Vedas Add Up: A Homegrown Mathematical System can help crack the Common Admission Test with ease" by Ms Alpana Sharma.


An article on Vedic Mathematics will be published in the January/February edition of "Hinduism Today" published by Hindu Press International.


Thanks to Barbara Salmon for the following quote about writing numbers with the units on the left, as discussed in the last Newsletter. I wonder how they did their arithmetic.

NUMBERS The Universal Language ISBN 0 500 30080 1 Denis Guedj 1996 (£6.95)
"In 458 there appeared an Indian treatise on cosmology, written in Sanskrit: the Lokavibhaga, or The Parts of the Universe. In it the number fourteen million two hundred and thirty-six thousand seven hundred thirteen was written, using the place-value system and requiring only eight digits: 14,236,713. In the text the digits were written entirely in letters and from right to left: "three, one, seven, six, three, two, four, one." The word sunya, void, which represents zero, also appeared. This is the earliest known document to use what we now know as Indian positional notation."


Courses are available in Singapore. Take a look at the web site of Vedic Publishing and Mktg Consultants/Vedic Mathematics International (S) Limited which is at www.vedic2000.com


If anyone knows of any Vedic Mathematics books in German please let us know.


There have been a number of developments following the successful series of seminars at Skovde University in October. We will keep you informed. Many thanks to Thomas Dahl who organised these events.


There are now between 400 and 500 on our mailing list. These are people all over the world and from many different backgrounds as far as we can judge; schoolchildren, teachers, lecturers, engineers, maths enthusiasts and so on.

Please note that if it is not possible to deliver a Newsletter on two consecutive occasions your address will be deleted from the mailing list.

Apologies for the duplication of Newsletter 12, steps have been taken to ensure this will not recur.


Your comments about this Newsletter are invited.
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?

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7th December 2000


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