Sutras - What are they?
Sutras are defined as “peculiar form of writing which aims at utmost brevity and often uses a poetic style to capture the essence of an argument or result. …" (see p 225, [1]).
Characteristics of Sutras
- Captures essence of an argument/result; avoids use of verbs and uses compound nouns
- Often poetic in style.
Examples of Vedic Math Sutras and Their Application
- All from 9 and last from 10 - Nikhilam Navastat Charamam Dashatah
- Useful in special case multiplication
- One more than previous - Ekadhikena Purvena
- Useful in
- Special case squaring (numbers ending with '5')
- Divisibility (osculation)
- Vulgar fraction evaluation - Recurring decimals
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Vedic Math Sutras
As reformulated by Swami Bhratikrishna Thirtha (1884-1960) the discoverer of Vedic Math, the list of sutras below is taken from the book Vedic
Mathematics (Motilal Banarasidas, 1965),
which includes a full list of the sixteen Sutras in Sanskrit. In some cases
a Sanskrit translation is not given in the text and comes from other
sources (see for instance Williams, K., Discover Vedic Mathematics, Motilal Banarasidas, 4th Edition,
2002).
The main sutras are sixteen in number and are given in table below:
Sutra
|
Translation
|
|
One more than previous.
|
|
All from 9 and the last from 10.
|
|
Vertically and Crosswise
|
|
Transpose and Apply
|
|
If the Samuccaya is the Same it is Zero
|
|
If One is in Ratio the Other is Zero
|
|
By Addition and by Subtraction
|
|
By the Completion or Non-Completion
|
|
Differential Calculus
|
|
By the Deficiency
|
|
Specific and General
|
|
The Remainders by the Last Digit
|
|
The Ultimate and Twice the Penultimate
|
|
By One Less than the One Before
|
|
The Product of the Sum
|
|
All
the Multipliers
|
The Sub Sutras are fourteen originally thirteen in the book. The formula 'On the Flag' is not in the list in the book Vedic
Mathematics but is referred to in the table
below :
Sub Sutra
|
Translation
|
|
Proportionately
|
|
The Remainder Remains Constant
|
|
The First by the First and the Last by the Last
|
|
For 7 the Multiplicand is 143
|
|
By Osculation
|
|
Lessen by the Deficiency
|
|
Whatever the Deficiency lessen by that amount and set up
the Square of the Deficiency
|
|
Last Totaling 10
|
|
Only the Last Terms
|
|
The Sum of the Products
|
|
By Alternative Elimination and Retention
|
|
By Mere Observation
|
|
The Product of the Sum is the Sum of the Products
|
|
On the Flag
|
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REFERENCES
[1] Joseph, G.V., Crest of the Peacock: Non-European Roots of Mathematics, Princeton and Oxford Press, 2001.
[2]Bharathi Krishan Thirtha, Vedic Mathematics, Motilal Banarasidas, 1965 (20 editions).
[3] Williams, K. R., Discover Vedic Mathematics, Motilal Banarasidas, New Delhi (first Indian Edition), 2006,
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