VEDIC MATHEMATICS NEWSLETTER
ISSUE No. 30
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 consists of a series excerpts from a research paper of 76 pages carried out last year by Mala Saraswathy Nataraj at the University of Auckland, New Zealand. The paper begins with a description of the Vedas, traces the development of mathematics in India from the pre-Vedic period to the medieval period and concludes with an examination of the book ‘Vedic Mathematics’ by Sri Bharati Krishna Tirthaji Maharaj. This is a thorough and well-written study and Mala intends to continue this research.
Vedic mathematics offers an intuitive and interesting way to teach and learn mathematics and provides a fresh insight into our number system. I believe these strategies have pedagogical value and will increase students’ understanding of arithmetic and algebra. Mathematics is a key element in the furthering of science and technology. In an era when interest in mathematics is flagging, a new approach is welcome.
The impact of Vedic mathematics in mathematics education remains largely unexplored. There is scope for research in this area, which will be beneficial to many. (from the Introduction)
Mathematicians in general, including Indian academics (Shukla, 1994; Dani, 1993) who have been strongly critical of Sri Tirthaji’s book, however agree on the sutras’ use in education. I believe the methods/sutras detailed in the book are relevant to the New Zealand mathematics curriculum and are useful in the teaching and learning of topics such as arithmetic and algebra in schools. The sutras certainly provide a fresh insight into our number system. (page 3)
Sutras are particularly relevant in education today as students have to understand and assimilate vast quantities of scientific information. Students’ ability to squeeze information and processes into compact units and to treat these units as objects to be operated upon, help in the acquisition of new mathematical ideas. They need to be able to recognise an idea at a glance and manipulate it as a whole (Kieran, 1992). Much has been written on this topic (Crowley, Thomas & Tall, 1994; Dubinsky, 1992) and it is significant that Sri Tirthaji has used the sutra style to capture his methods or rules. (page 15)
The Indian tradition of mathematics is essentially inductive and so rigorous proof is rarely stated clearly. Debroy (1993) also calls attention to the fact that the inductive-cum-intuitive approach is evident in some of Ramanujan’s work. When Bhanu Murthy (1992) attempted to prove some of Sri Tirthaji’s formulae, he found a few profound theorems of number theory involved.
Irrespective of the difficulty of establishing its historical validity, George Joseph argues that the methods in the book provide an original and refreshing approach to subjects that are often thought to be mechanical and tedious.
Bhatnagar has made some pertinent observations on the scope of the book’s pedagogical applications in his paper.
“The ingenuity and simplicity of these rules impressed the present author so much that he decided to prepare the present paper with the sole aim to bring this wealth of ideas to the notice of as wide a mathematical community as possible.” (page 31)
All the mathematicians involved in the debate are in agreement that the methods can be put to good use in teaching and learning in middle and high schools. The wisest course at present seems to be to keep an open mind about both the origins and the claim that the sutras cover all mathematical topics. (page 32)
Big numbers are abstract for the reason that they are not available for immediate arithmetical computation but they are concrete by virtue of being particular numbers. As such, they can serve as a bridge between arithmetic and algebraic reasoning. Consideration of particular examples that help to generalise could lead students to a structural insight. (page 68)
VISIT FROM NEPAL
Krishna Subedi, the Principal of a school in Kathmandu (the capital of Nepal), visited England for about two weeks in March. Krishna founded this school in 1996 and it is now flourishing with about 400 students aged from 3 to 16 years. He recently became interested in Vedic Mathematics and has given talks and written articles which have been very well received in Nepal. He intends to introduce the Vedic system in his school soon.
During his visit to England Krishna attended some workshops on Vedic Mathematics in London and visited St James School in London and the Maharishi School in Skelmersdale, Lancashire. Vedic Mathematics is taught at both these schools.
Krishna is also studying for an M.Ed. at Endicott College Massachusetts, U.S.A. and as part of this he will be conducting a detailed statistical analysis between classes taught Vedic Mathematics compared to classes not taught it. This is just the sort of research that is needed to demonstrate the effectiveness of the Vedic system and we look forward to hearing about the results. We will keep you informed. If you would like to make contact with Krishna Subedi his email address is
SUPREME COURT JUDGEMENT IN INDIA
We have been sent more information on this by Mr Jain at Motilal Banrsidass. The National Curriculum Framework for School Education (NCFSE-2000) was formulated and released by the National Council for Education &Training (NCERT) in November 2000. NCERT was set up by the government in 1962 to assist and advise the Central and State governments on academic matters related to school education. Following its release various political extremists launched a campaign of misinformation due to their misunderstanding of the content. Newspapers were flooded with articles highlighting the alleged perfidy of the government as were prime chat shows on the TV. Vedic Maths and Vedic Astrology were being imposed, they said.. The various parties then joined forces to file a PIL in the Supreme Court to stall the implementation of NCFSE-2000. However all three judges rejected outright the seven baseless made by this group.
Nikhilam sutra applied to hexadecimal numbers
From Chandrahas M. Halai.
You will be glad to know of the recent development in my computer science course.
You must be well aware of the fact that computer engineers extensively use hexadecimal numbers to represent large binary numbers and patterns of bits. Recently I taught the concepts of complements and the Nikhilam sutra to my students in the computer science & programming course (negative numbers are represented in computers as 2’s complement numbers, i.e. 256’s complement for a one-byte value, 65636’s complement for a 2-byte value) and also showed how to apply the concept of complements & nikhilam sutra to easily multiply hexadecimal numbers. The concept has been well received by the students and as well as the teachers.
Chandrahas Halai is a computer aided Mechanical Engineering consultant based in India. He runs an institute which trains engineers in advanced systems programming and is now doing research in the field of applying VM to solving problems in Engineering & especially Computational Fluid Dynamics. Recently he has been appointed as the lecturer of mathematics at Indian Planetary Society (IPS), founded by DR. J J. Rawal, who is a renowned Astrophysicist, and is looking forward to applying VM to Astronomy.
EXPANSION OF VEDIC MATHEMATICS
Following the recent founding of the World Academy of Vedic Mathematics steps are being taken to set up global contacts who could oversee and set up workshops in their country. If you would like to be the contact in your country or area, or would like further information, please can you let us know. Either contact the Academy directly: Mr S. R. Agarwal, , or contact us at
ADVANCED TEACHER’S MANUAL AVAILABLE
The third Manual in this series is now ready. It is most suitable for teachers who teach students aged 13 to 18 years and is based on week-long summer courses given at Oxford University for several years to Swedish mathematics teachers. Details can be found at www.vedicmaths.com
VM TUTOR IN MUMBAI
Govind Bahroos is conducting classes of Vedicmaths in Mumbai and teaching children above the age of 10 years. Till now 120 students have been trained. He has also given speech on vedicmaths in Rotary & Rotract Club. He lives at Andheri Area (Ph: 022-2634-8911), runs Aromatic Chemicals factory in Kanjur Marg(Ph: 022-2578-2352), and teaches for one to two hours in the evenings. E-mail:
Visit our ‘Tutors’ page at www.vedicmaths.org
WORKSHOPS IN INDIA
If you want to know about Vedic Mathematics Workshops or research in India send an email to Mr R. P. Jain at
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
Some articles from previous newsletters are:
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 6: The Sutras of Vedic Mathematics
Issue 7: The Vedic Square
Issue 8: The Nine Point Circle
Issue 11: Is Knowledge Essentially Simple?
Issue 14: 1,2,3,4: Pythagoras and the Cosmology of Number
Issue 16: Vedic Matrix
Issue 17: Vedic Sources of Vedic Mathematics
Issue 19: “Maths Mantra”
Issue 20: Numeracy
Issue 21: Only a Matter of 16 Sutras
Issue 22: Multiplication on the Fingertips
Issue 23: India’s System of Mental Mathematics
Issue 24: The Sign of Nine
Issue 25: Maharishi’s Vedic Mathematics
Issue 26: Foreword
Issue 27: The Absolute Number
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Editor: Kenneth Williams
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22nd March 2003