Friday, July 6, 2012

Vedic maths. Facts + fiction = fantastic

It has been said that truth is stranger than fiction.  That is certainly true when it comes to the story of the origins of “Vedic” maths.  

Vedic mathematics first came to light in a book published in 1965 by the impressively named Bharati Krishna Tirthaji - an Indian mathematician ...and mystic. Tirathji claimed to have rediscovered Vedic mathematics after meditating on some neglected sacred scripts. This is where the story gets a tad bizarre - for there is no evidence in the Sutras of anything vaguely resembling the mathematics that Tirthaji proposed.  He is reported to have spent eight years meditating in a forest in order to discern the hidden mathematics.  This has been likened by Alex Bellos, author of “Alex’s Adventures in Numberland”, as  being akin to a “...a vicar announcing he had found a method for solving quadratic equations in the Bible”. When challenged by other Indian mathematicians who could read Sanskrit to identify the passages upon which he based his mathematics Tirthaji claimed that the messages were in his texts and in no other.  There was also mention of a 16 volume manuscript that Tirathji had written dealing with the subject - but which had somehow been lost prior to publication - indeed prior to him sharing it with a single other person. Such loss apparently did not disturb Tirathji who simply said he would re-write it from memory.  The first, and only book published (posthumously) was but a fraction of the mathematics that he claimed to have re-discovered in the sacred texts.   (A detailed discussion on the story of the “discovery” of Vedic mathematics can be found here.)  

In short, it appears unlikely that the mathematical techniques mentioned were “discovered” in any ancient Vedic text.  Intrigued by the power and simplicity of the mathematics Alex Bellos did some research to see if the techniques had been mentioned elsewhere, and it turns out that one of them, Vertically and Crosswise,  had been published in none other than Fibonnaci’s Liber Abaci (published in 1202 and credited with introducing Hindu-Arabic numerals and calculation techniques to Europe).  Another, All from 9 and the last from 10,  was apparently  a wide spread technique in Europe in the sixteenth-century - so wide spread that it may have been the origin of our current symbol for multiplication.

However, although many would find the story of the “re-discovery” of Vedic mathematics fanciful it is undeniable that the approaches  described in Tirathji’s text actually work.  In some cases they are no more efficient than contemporary approaches but in others they clearly are.  

Two of the techniques describes as “Vedic” maths that can be traced to European sources are All from 9 and the last from 10 and Vertically and Crosswise. Both are worth exploring.

All from 9 and the last from 10 is essentially a quick mental maths trick with limited application - the approach as depicted here can only be used when subtracting numbers from multiples of 10 (in other words 100, 1000, 10 000 etc.) 
but with minor modification can be used with any number ending in zero.  However it is useful in illustrating the nature of Vedic maths.  With this approach to subtraction you work from left to right and subtract all digits being subtracted from 9 except for the last digit which is subtracted from 10.

1000 - 578 becomes

-  578 (SUBTRACT the 5 and 7 from 9 and the 8 from 10)
= 422

Although limited in application it is easy to see how this might be a useful skill when using money for example.

A technique with wider application is  Vertically and Crosswise which allows rapid calculation by multiplication. Consider 63 x 28. The Vedic method would be;

Step 1. Write the digits being multiplied on top of each other.

6 3
2 8

Step 2. Multiply the numbers in the right hand column (24).  Write the 4 in the units column and carry the 2.

6 3
2 8
                                                                   2  4
Step 3.  Multiply diagonally opposite numbers (cross-wise) and then add the products (multiply 6 X 8 = 48, 2 X 3 = 6, 48 +6=54.  Use the carried 2 from the previous stage = 56. Write the 6 and carry the 5

6 3
2 8
                                                                5  6 4
Step 4. Multiply the left hand column (6 x 2 = 12)  Add the 5 being carried (12 + 5 = 17). Write the 17 to the left of the answer thus:

6 3
2 8
                                                               1 7 6 4

For those who prefer a more visual explanation this video gives a good indication of how the process works.

At first glance using two digits like this the process might easily be dismissed as a novelty and only marginally more efficient than  the “traditional” approach.  But when three or four digit numbers are being calculated (or indeed any  large number) the same method is employed and needs only one line of working.  It is much quicker than the standard approach to this problem - much more efficient.

Those wishing to explore some of the techniques might like to visit this site which provides opportunities to practice some of the techniques and this link to a free manual for teachers. This latter resource contains much that is not purely related to “vedic mathematics” and offers some sound techniques for teaching mental calculation techniques.There are more techniques than presented here to examine and explore - far more than could be presented in a post such as this.

I believe it would be unwise to teach this approach to young children. However, to students who have been introduced to and understand the principles and concepts of conventional mathematics this approach might add interest  and intrigue - and would promote mathematics as something worthy of exploration.    

There is much of worth in Vedic mathematics.  The murky story of its “re-discovery” should allow the story teller that is  in every effective teacher to create the setting for some effective exploration of mathematics.  At worst it still has to be better than providing yet another worksheet...

If you enjoyed this post you may enjoy my other maths related posts available via the maths page or by clicking here.

1 comment:

  1. hey,
    Nice information shared ,, vedic math is just a tecnique to calculate fast so there is no harm to learn it as soon as possible..
    To learn fast and solve the problems in limited period of time vedic mathematics playes an important role. It can be applied in competitive exams.
    and now its easy to lean vedic math online also one of the site I came across was
    This vedic math online course may be helpful for all those who are scared of mathematics.