ISSUE No. 78
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 article is from Robert McNeill who has taught mathematics for over 40 years to students aged from 5 to 18. He is currently Headmaster at St James Independent School for 3½ to 11 year olds in Stockport, UK.
WHY ARE THERE 16 SUTRAS?
The question sometimes arises as to why there are 16 sutras? The first obvious answer may be perhaps this is just how many are needed to cover the whole range of mathematics. But could there be some other significance?
The number 16 arises in several places in the ancient Vedic tradition. For
instance, there are 16 svara (vowels) in the Sanskrit alphabet, if all measures
are included. These are:
[ a (short and long), i (short and long), u(short and long), ri (short and long), lri (short and long), e, ai, o au, am, ah. ]
These 16 svara are said to represent the 16 matrikas (measures) or shaktis. A shakti is a great power that may manifest through a being in appropriate circumstances. In The Secret Of The Three Cities, a seminal treatise on Tantrism, the following examples of shakti are enumerated:
Aisvarya (empowerment), dharma (law), yashas (fame), prosperity, knowledge and discrimination.
It is said that Krishna manifested all 16 shakti whilst Rama is said to have manifested seven. Apparently, even one would give rise to a Shakespeare, an Einstein or possibly a Jagadguru (world teacher) such as Bharati Krsna Tirthaji.
Monier-Williams, in his Sanskrit to English Dictionary gives further examples such as kanti (beauty), daya (sympathy), tushti (contentment). In verse 10 of The Secret Of The Three Cities the 16 svara are shown to be placed in a chakra diagram and are said to relate to the tithi i.e. the phases of the moon. In the commentary, it is explained that the phases of the moon are 15, characterised by waxing and waning, with sadakya ( literally, "said always to exist") being without waxing and waning, is the cause of the other 15.
The number 16 also occurs as one of the most common Sanskrit chanting metres known as the sloka or anushtubh metre. This is the main metre found in the great epics of the Mahabharata and Ramayana. In this form there are two lines of 16 syllables each, making up four padas of eight syllables. There are very precise rules for the accents within the 16 syllables but once again the number 16 is the key. As a further example, it is interesting to note that, in Hindu money, there are 16 annas equalling one rupee and the reader may enjoy Bharati Krsna Tirthaji's chapter on Practice and Proportion in his text Vedic Mathematics.
Thus we see that the number 16 occurs in astronomy, in metre, in the science of pronunciation and other areas. We get a sense of the unity through the great tradition covering several aspects of the Veda and Vedanga.
Arguably however, the most profound and certainly the most ancient of the references to 16 in the Vedas is found in the Prashna Upanishad, part of the Atharva Veda. "Prashna" means "question" and there are enumerated six questions on the nature of the Brahman. The final and last question asked is about a Vedic divine being called "Shodashakala Purusha" or "Person with sixteen divine attributes". Pippalada answers that Shodashakala Purusha is within the body and explains its greatness and says "So far do I know this Highest Brahman, there is nothing higher than it".
The sixteen attributes or limbs are listed in the fourth question as:
5 organs of knowledge (the senses);
5 organs of action (speech, handling, procreating, excreting and walking);
4 aspects of the inner organ of mind (manas, buddhi, citta and ahankara);
The skin giving lustre (as distinct from the sense of touch) and the Pranah (breath) which holds everything together as a string in a necklace.
Shankara in his commentary on the Prashna Upanishad points out that whilst the Purusha (the divine person within all) appears to consist of 16 parts nevertheless it is one, totally attributeless and non-dual.
So, according to the Atharva Veda, the number 16 is at the heart of all beings in the creation. Therefore it isn't surprising that its manifestation in so frequent and maybe Bharati Krsna Tirthaji himself came to know that Purusha through long years of study and personal discipline in the forest.
NEW E-GURUKUL TEACHER TRAINING COURSE
We are delighted to announce that a certificated teacher training course in
Vedic Mathematics will be starting on 3rd March 2012. The programme is only
open to applicants who have some teaching experience (though that can be in
any field). To apply for this course please visit:
PREVIOUS E-GURUKUL COURSE
The previous teacher training course ended on 18th December 2011 and was a tremendous success. The level of commitment and enthusiasm shown by the students was really inspiring. You can see their comments at: http://e-gurukul.net/portal/vmttc-batch-2-results
VERA STEVENS IN LONDON
As mentioned before in this newsletter Vera has done remarkable work in teaching children in the youngest grades. Vera will be in London in the latter part of June this year and would be glad to meet any primary school teachers who are interested in her approach. Please contact: firstname.lastname@example.org
Brian McEnery is in the process of publishing material on the development of
an animation system for teaching mathematics.
"CHILDREN 'OVER-RELIANT ON CALCULATORS' IN MATHS LESSONS"
FIBONACCI AND DIGIT SUMS - from Vera Stevens
Take the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 . . .
in which each number starting with the third one is the total of the two previous numbers (e.g. 13 + 21 = 34).
Many remarkable properties of this sequence have been discovered, including amazing connections with nature. Here is one which seems to be new.
Convert this sequence to its digit sums:
1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8 9 . . .
Now subtracting each digit from the next digit you get the digit sums of the Fibonacci sequence again!
0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8 9 . . .
That is: 1-1=0, 2-1=1, 3-2=1, 5-3=2, 8-5=3, 4-8=5., etc.
How do we get 4-8=5? Since this is digit sum arithmetic you can use the 9-point circle and count back 8 units from 4 to arrive at 5. Or, since 4-8=-4 you can add 9 to -4 to get 5.
This property does not seem to apply to any other sequence I have tried. Can you find one?
THE VEDIC NUMERICAL CODE AND PI
A new page has been added at vedicmaths.org on this topic:
5 DAY COURSE IN KERALA, INDIA
SEMINAR IN MANCHESTER, UK - "MATHS WITHOUT TEARS"
This seminar "Maths Without Tears - the Magic of Vedic Maths" will
take place on Sat 18th February 2012 from 9-4pm, at Belmont House (St James
School), Stockport SK4 1TG. To book or for more information email: email@example.com
or go to:
ARTICLE: HOW VEDIC MATHEMATICS ADDS UP SO WELL
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 firstname.lastname@example.org
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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
11th February 2011