**Vedic Mathematics Newsletter No. 121**

A warm welcome to our new subscribers.

This issue’s article (at the end of this newsletter) is titled “All Methods are Vedic”, and discusses what is meant by a ‘Vedic’ method.

“This apparent paradox can be resolved by considering that there can be a scale of ‘Vedicness’. That is, that one method may be more Vedic than another, or less Vedic.”

******************************NEWS******************************

**5TH ONLINE CONFERENCE**

This event will be on 16^{th} and 17^{th} March 2019.

Everyone is invited to speak or watch, and as usual the Conference will feature speakers from around the world telling us of initiatives in various countries. There will also be VM Workshops, and presentations outlining recent research.

Details about registration, how to offer to make a presentation, submit research papers etc. will be posted shortly on the websites:

__https://instituteavm.wixsite.com/__

__http://www.vedicmaths.org/__

which will be updated over the coming weeks as the details are finalised.

**TEACHER TRAINING COURSE STARTS 21**^{ST}** JANUARY 2019**

This popular 9 week course consists of 36 video lessons, 9 tests and two assignments, plus discussion forums and optional challenge material.

See details at:__http://courses.vedicmaths.org/Teacher_Training_Course.html__

PRODUCTS USING SYMMETRY

We can find products using symmetry with the Sutra *By the Deficiency*.

Suppose we require the product 29 × 24.

We can think of the numbers as part of a sequence of consecutive integers:

. . . . 30, *29*, 28, 27, 26, 25, *24*, 23, . . . .

Noticing that 29 is 1 below 30 we may ask if we can get the product 29 × 24 from the product 30 × 23, where 30 is *1 more* than 29 and 23 is *1 less* than 24.

In fact 29 × 24 = 30×23 + 1×6 = 696,

where the 1 and 6 are the differences of the given numbers (29 and 24) from the base number, 30.

This makes such products very easy to find and is proved by: (*B*+*a*)(*B*+*b*) = *B*(*B*+*a*+*b*) + *ab*, where *B* is the base chosen and *a *and *b* are the deviations from that base.

Similarly, if we wanted 28 × 24 we could again use 30 as base, and to preserve symmetry we would need to pair it with 22 (2 below 24).

Then 28 × 24 = 30×22 + 2×6 = 660 + 12 = 672.

If the base number falls *between* the two given numbers, as in 58 × 63 (here we can use a base of 60), then one of the deviations is positive and one negative, so we get:

58 × 63 = 60 × 61 – 2×3 = 3660 – 6 = 3654.

[We imagine the sequence of numbers from 58 to 63, and since 60 is 2 closer to the centre we need to pair it with 61 which is also 2 units closer to the centre.]

This method is useful in permutations and combinations where the product of a series of numbers is needed. To find _{33}P_{4} = 33×32×31×30, for example, we easily get the product of the outer pair of numbers to be 990. The product of the inner pair is then 2 more by the above method, i.e. 992.

990×992 is easily found using a base of 1000. So _{33}P_{4} = 982080.

[A paper on evaluation permutations and combinations will be presented at the upcoming March conference.]

Kenneth Williams

**ONLINE JOURNAL ARTICLE – “Powers of 9”**

A new article has been published in the Online Journal:

"Powers of 9" by M Rajagopala Rao.

This paper shows how the coefficients in Pascal's Triangle can be used to easily obtain powers of 9.

See the article here:

__http://www.vedicmaths.org/resources/journal-of-vedic-mathematics__

***********************************************ARTICLE FOR NEWSLETTER 121***********************************************

**All Methods are Vedic**

**Kenneth Williams**

Sri Bharati Krishna Tirthaji was the 143^{rd} Shankaracharya at Puri, India. In 2008 I had the opportunity to put some questions on Vedic Mathematics to the 145^{th} Shankaracharya at Puri: His Holiness Jagadguru Shankaracharya Swami Nishchalananda Saraswati.

One thing which he said to me which made a significant impression was “All methods are Vedic”. This rather puzzled me as I had come to think of methods which are Vedic and methods which are not. For example at the end of Chapter 20 of his book^{1} Bharati Krishna writes “In all these processes there is an element more or less, of clumsiness and cumbrousness which renders them unfit to fit satisfactorily into the Vedic category.”

And in Chapter 37, referring to Pythagoras’ Theorem, he says “There are several Vedic proofs, every one of which is much simpler than Euclid’s etc.”

These comments and others indicate that Bharati Krishna considered there is a distinction between Vedic and non-Vedic methods.

So the question naturally arises as to how these two enlightened gentlemen could be contradicting each other, if indeed there is a contradiction.

This apparent paradox can be resolved by considering that there can be a scale of ‘Vedicness’. That is, that one method may be more Vedic than another, or less Vedic.

So when Bharati Krishna (e.g. Chapter 28) compares the ‘current method’ or the ‘usual method’ or the ‘conventional method’ with the ‘Vedic method’ it is simply a way of comparing a current method with a simpler one shown in his book.

This is confirmed by statements like “All these methods, however, fall in one way or another, short of the Vedic ideal of ease and simplicity” (page 348, chapter 36). So we are led to understand that one method may be ‘more Vedic’ than another, with the ideal of ease and simplicity at one extreme.

**The Vedic Ideal**

This means that we cannot say that this method is Vedic and this is not: only that one may be more Vedic or less so.

Consequently:

a) any method that leads to a correct solution would be classed as Vedic,

b) there is no dichotomy e.g. ‘this is Vedic and this is not’,

c) one method may be closer to the Vedic ideal than another.

Other references to the Vedic ideal are:

Page 84:

… the Vedic system's Ideal of "Short and Sweet".

Page 85:

… the Vedic ideal of ideal simplicity all-round and which in fact gives us what we have been describing as "*Vedic one line mental answers*"!

Page 240:

… the Vedic ideal of the at-sight mental-one-line method of mathematical computation.

Also on page 240 we may note:

… from the Idealistic Vedic standpoint.

… the highest Idealistic ideal of the Vedic Sūtras.

To summarise then we may say that any method that correctly solves a problem may be classed as ‘Vedic’, but some methods are more Vedic than others. The closer a method is to the Vedic ideal of ease and simplicity etc. the more Vedic it is.

^{1} All references are to Sri Bharati Krishna Tirthaji’s book “Vedic Mathematics” first published in 1965. Page references are for editions prior to 1992.

End of article.

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Editor: Kenneth Williams

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10th January 2019