Issue129 - Research in Vedic Mathematics

Vedic Mathematics Newsletter No. 129

A warm welcome to our new subscribers.

Answers to the puzzles from the previous newsletter are: 2021 = 43 × 47; 2491 (=47×53); 119, 120

This issue’s article is by Kenneth Williams, newsletter editor, and is titled “Research in Vedic Mathematics”.

Research can be very worthwhile: it focuses the mind, expands creativity and, hopefully, leads to something useful.“





The Institute for the Advancement of Vedic Mathematics (IAVM) website is at but please note it is being rebuilt and will be up and running sometime in March.

IAVM email:

Four events are announced below.

Knowledge Series Webinars

Commencing 13th March

A series of six free webinars throughout the year on mathematical understanding from ancient India and mathematical practices in diverse cultures.

13th March

Exploring ancient Indian mathematics: From zero to infinity
Prajakti Gokhale  

In this session, we will explore the journey of ancient Indian mathematics from Indian subcontinent to Europe. We will understand the timeline of ancient Indian texts and important contributions by Indian mathematicians. Prajakti will also demonstrate some key techniques and practical applications. The talk will conclude with views from mathematicians around the world on the merits of ancient Indian mathematics.
Register here to attend.

Further talks will be announced on our website.

Masterclasses for IVMO

10th, 11th, 17th, 18th April

Continuing from last Autumn, four masterclasses will be given by James Glover dealing with further VM techniques in preparation for IVMO 2021.
Topics covered: Squaring, Cubing, Coordinate Geometry, Combined Ratios, Scale Factors, Algebraic Division, Binomial Expansions.

 7th Annual Online Conference

11th – 12th June

The conference will be held across two days. The first day will be given over to presentations of papers and presentations of how best to deliver mathematics online.

The second day will comprise free workshop sessions for students of different grades as well as teachers. Student workshops will include activities and puzzles together with a poetry competition. Further details will be sent in due course.

International Vedic Maths Olympiad (IVMO 2021)

11th September

Postponed from 2020, IVMO 2021 will now take place in both online and paper format. Both formats have multiple choice formats. Further details will be sent to Regional Coordinators in due course. Please email us if you want to be a Regional Coordinator.



Recent research by Brian G. Mc Enery has led to the development of new software designed to investigate the potential for using Pythagorean Triples, in a modern computational environment.  The software development is based on Kenneth Williams’ book Triples and has led to the development of Python classes for Triple and CodeNumber objects. The software is also being developed using Jupyter notebooks, as a way of developing a dynamic interactive presentation. At present the software is located in a git repository, and the notebook may be viewed at,



  1. "Continued Fractions using the Sesa Sutra"

by Kenneth Williams, 2021

One of the Sūtras of Vedic mathematics is shown to have useful applications in various ways in relation to continued fractions. We see how to easily convert a given fraction to a continued fraction and vice versa, how to get the convergents and the accuracy involved in switching to any given convergent. Some applications of continued fractions are also briefly described.

  1. "Highest Common Factor and Lowest Common Multiple using the Sesa Sutra"

by Kenneth Williams, 2021

This paper shows how to obtain highest common factors and lowest common multiples of two or more numbers, using the Vedic Mathematics Sutra The Remainders By the Last Digit. Includes applications to polynomial expressions.



The Advanced Diploma course starts on 29th March 2021.

The next Teacher Training Course is scheduled for 24th May 2021.

For details of these and the several other courses offered by the VM Academy please see:



This course takes up the subject of triples, like 3,4,5, which represent the sides of right-angled triangles (e.g. 32 + 42 = 52). Most of the techniques developed though are not restricted to integer-sided triangles. We see how to find two sides of a right-angled triangle given only one side, and the many applications of this, including in equations, in 2 and 3-dimensional geometry and astronomy. The course is independent of any other of our courses and the content is not repeated in any of them. No calculator required. See further details here.



Copyright has now expired on the book “Vedic Mathematics” by Sri Bharati Krishna Tirthaji. This is the original work, first published in 1965, that has inspired much subsequent research (and also controversy). This book is now available in pdf format, with errors corrected and indexes etc., for anyone who wishes to request it.






Vedic Maths research is going on all around the world. This is clear from the articles appearing in journals, conference papers, magazines etc. from many individuals.

From time to time we get questions about research: what to study, how to study, how to publish, and so on. So here is some brief guidance for those interested in pursuing research in this fascinating subject which has such high potential for research opportunities.

What to Study

Research can be very worthwhile: it focuses the mind, expands creativity and, hopefully, leads to something useful.

Obviously, a subject of research must be chosen and I generally advise that it should be either a topic that you are very familiar with (i.e. know in some depth) or one which you have a special interest in. Preferably both of these.

There are many topics in Tirthaji’s book that could be followed up. Looking at the amazing Vedic methods and practising them often leads to thoughts about how they can be extended or applied in a different setting. Tirthaji himself gives many hints. For example, in Chapter 17 he writes: “This portion of the Vedic Sūtras deals also with the Binomial theorem, factorisations, factorials, repeated factors, continued fractions, Differentiations, Integrations, Successive Differentiations, Integrations by means of continued fractions etc.”.

There are several other such comments in the book, in particular the two lists in Chapter 40 are of special significance.

How to Study

To carry out the research you need to know your chosen subject thoroughly and you need to know Vedic Maths thoroughly. It is really essential that you know VM very well and have a feel for what a VM approach to a problem would be like, i.e. holistic, simple and directly related to the Sutras. Look for unifying principles in your research.

Understand that there are likely to be setbacks, disappointments etc. You may find that after considerable effort and time you have discovered something that was obvious or that has been found by someone else previously. So above all be determined to continue in spite of these events.

Put the study aside for a while if it is going nowhere, and return later. And you should not rush, this really does reduce the creative faculties.

On the other hand you may have too many ideas. Writing the ideas down will help to consolidate and clarify what is important and weed out less useful points. In time these will organise themselves.

To keep the mind still and clear some form of meditation is highly beneficial. Get to know how your mind works and use this to help direct your study.

If you get a nice result, you may be tempted to stop studying and write it up – this often happens. But maybe if you look further your result may be a clue to something deeper. See if it is part of a bigger picture.

Write-up and Publication

Look at VM articles that have been published to get an idea of expected format, length etc. and follow any guidelines that your intended publisher expects. For example:

Make sure there are no errors; it gives a poor impression when an article has mistakes.

Check your work is original by searching online and asking those working in the same field as you for advice.

Give references to any work cited in your paper, it will be assumed that you are claiming authorship of any material you do not ascribe to someone else. Similarly for proofs: include proofs of results or theorems you have used or give references.

For publication of Vedic Maths articles there is the online International Journal of Vedic Mathematics (see link above) and Vedic maths conferences. There are currently two annual conferences: online and in-person. These are organised by the Institute for the Advancement of Vedic Mathematics who can be contacted for more information.

End of article.


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 at

Previous issues of this Newsletter can be viewed and copied from the Web Site:

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Editor: Kenneth Williams

The Vedic Mathematics web site is at:


3rd March 2021


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