Issue 108 - The Sub-Sutras

Vedic Mathematics Newsletter No. 108

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This issue’s article (at the end of the newsletter) is by Kenneth Williams and discusses the role of the Sub-Sutras of Vedic Mathematics.



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The journal of the Institute of Mathematics and its Applications, "Mathematics Today", has published an article on ‘Teaching Calculus’ by Kenneth Williams.

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The Sub-Sutras

Bharati Krishna makes it clear that the “Sixteen Simple Formulae from the Vedas” give “One-line Answers to All Mathematical Problems”.
So what is the role of the sub-Sutras? Why are they necessary and how do they fit into the Vedic system?
Here I would like to suggest answers to these questions and, as usual, would be glad to hear your views whatever they are.

A Sutra is a general expression of some principle, and being general it has a wide range of more specific expressions. The sub-Sutras, I suggest, describe these more specific expressions.
For example, the first Sutra is By One More than the One Before, and it has many applications – wherever something is generated from something else.
More specifically we may see proportion as a special case of Sutra 1, in which a ratio generates a further quantity. So the use of the sub-Sutra By Proportion indicates that a ratio is applied and a result obtained.
Sub-Sutra 1 (By Proportion) then is intricately related to Sutra 1 (By One More than the One Before).

Immediately above the lists of Sutras and sub-Sutras in BKT’s book is the heading “Sixteen Sutras and Their Corollaries”. A corollary is a statement that follows from a previous statement. So this heading implies the same thing: that the sub-Sutras are each related to a Sutra.

This interpretation of the sub-Sutras implies that each sub-Sutra is related to at least one Sutra, and in fact derived from it. It also implies that there is no definite number of sub-Sutras. BKT does not say there is some fixed number of them and in fact it was said of him that he would pluck sub-Sutras out of the air.
This makes a lot of sense since BKT has made it very clear that the 16 ‘mathematical formulae’ give one-line answers to all mathematical problems. Hence there is no need for any further Sutras and so the sub-Sutras must be included within the Sutras themselves.
The interesting question that arises from this is: how does each sub-Sutra in BKT’s book relate to one or more of the Sutras?
Comments etc. on this can be sent to and can be published in later newsletters.

End of article.

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Editor: Kenneth Williams

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12th June 2016


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