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VEDIC MATHEMATICS NEWSLETTER ISSUE No. 9 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. ***************************** This issue's article: This is written by Barbara Salmon who has been researching pattern in number and Vedic Mathematics for some years. THE VEDIC TRIANGLE The Vedic Triangle, contains the same numbers and number patterns as the Vedic Square (see Newsletter number 7), but laid out in the shape of a triangle. There are two main steps:-
When treated as exercises, steps such as these offer a simple and interesting way to explore various aspects of number. Step 1: CREATING A MULTIPLICATION TRIANGLE We can create a multiplication triangle, by multiplying digits 123456789 x 987654321 (i.e. digits 1 to 9 as ascending and descending) using the 'Vertically and Crosswise' step sequence described in the original Vedic Mathematics Treatise (Chapter 3) by Sri Bharati Krsna Tirthaji. This gives us the product of every number by every other number, in the range 1 to 9. Following this step sequence automatically gives us the products, in the shape of a triangle. Here is a small example of that particular step sequence, using the first two digits of the multiplier 12, and multiplicand 98:- 1 2
x The step sequence is:- ( If we want the product of 12 and 98 we carry the 1 of 16 and 1 of 18 one column to the left to get 1176.) 9: 8: 16
The individual multiplication products now
form the If we extend the multiplication from 12 x 98 to 123456789 x 987654321 we have a multiplication triangle as follows:- 1
2 3
4 5
6
7 8 Viewed this way 'Vertically and Crosswise' is acting more like a 'modeling' tool for Number. The pattern of the Multiplicand and Multiplier together shape the pattern of the multiplication products. Exercise: Create your own multiplication triangle - using squared paper (or lined paper overlain at right angles), or the 'table' option if you have a text processing package on your computer. Colour in all the products of the five times table using the same colour. Step 2: REDUCE THE MULTIPLICATION TRIANGLE TO DIGITS SUMS To reduce a number to its Digit Sum, simply add the digits of the original
number together. Repeat the process if necessary until only one digit remains.
For example, 48 is 4 + 8 = 12, which is 1 + 2 = 3. Usually 'Digit Sums' are
used in arithmetic to cross-check results
Exercise: Copy out the triangle onto squared paper and colour in the numbers which correspond to the five times table products you highlighted in the Multiplication Triangle. Are/were you able to see the following ? :- The recognition of pattern in number, as illustrated by the types of exercise described above, helps us to develop our mental agility, improvise solutions and think for ourselves. You will see by visiting the Multiplication and Addition parts of the Creative Maths website, that 'Vertically and Crosswise' offers a broad range of multiplication styles (including the ones we commonly use today). The alternative styles were improvised by myself in March this year. Once the pattern was seen, - each style took a few minutes to develop. The only thing that is changing in each example, is the sequence of multiplication steps (which in all cases can be from left to right or right to left - or even a bit of both!) and the way we record the sums. The underlying principle is the same! This demonstrates great flexibility within what is undoubtedly a unified system - the system of Vedic Mathematics. Creative Maths website http://www.users.waitrose.com/~dabsalmon **************************** NEWS -------------------------------------- In spite of its simplicity and in spite of the extensive efforts of the most distinguished mathematicians since then, the problem has so far remained unsolved and has ranked with Fermat's Last Theorem as one of the great unsolved problems of mathematics. Dr Kapoor's book "GOLDBACH THEOREM" has just been published by M/s. Arya Book Depot, 30, Nailwala, Karol Bagh, New Delhi 110005 (INDIA), Phone : (00-91-11)5721221, (00-91-11) 5720363, FAX: (00-91-11)5767012. ISBN-81-7063-113-0. Price : Rs. 175/-. We have not yet seen this proof but hope to have a copy of the book soon. For his excellence and service rendered in the field of Vedic mathematics, Dr Kapoor has been awarded "Shri Guru Gangeshwaranandji Veda Ratna Puraskar-1997" by Bharatiya Vidya Bhavan, Bangalore. The Veda Ratna Puraskar as these are called have come to be accepted as highest epitomes of all honours that a Vedic scholar can strive to achieve in his life time. We have more details about this book and the author which will soon be made available on the web site. COURSES ON VEDIC MATHEMATICS ON THE TV AGAIN COMPARATIVE STUDY OF VM IN TEACHING A PhD student in the U.S. is also interested in making a study of the Vedic methods. REFERENCES TO THE VEDIC SQUARE Mathematics Teaching (UK teaching journal) Nos. 62, 63. The article in No. 62 is by Joseph Howse and the one in No. 63 is a response from R Thatcher. There are sections on the Square in the book "The Language of Pattern" by Albarn, Smith, Steele, Walker. Thames and Hudson, London, 1974. ISBN 0500231907. TRANSLATOR REQUIRED To subscribe or unsubscribe to this Newsletter simply send an email to that
effect to news@vedicmaths.com Visit the Vedic Mathematics web site at 7th July 2000 |
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