The Vedic Mathematics Sutras

This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in some cases a translation of the Sanskrit is not given in the text and comes from elsewhere. The Sutras describe mental processes as explained in the paper no. 57 here: "Structures in the Vedic Mathematics Sutras". These mental processes construct the mathematics.

The formula 'On the Flag' is not in the list given in Vedic Mathematics, but is referred to in the text.

The Sixteen Sutras


  Sutra Translation
 1  By one more than the one before
 2  All from 9 and the last from 10
 3  Vertically and Crosswise
 4  Transpose and Apply
 5  If the Samuccaya is the Same it is Zero
 6  If One is in Ratio the Other is Zero
 7  By Addition and by Subtraction
 8  By the Completion or Non-Completion
 9  Differential Calculus
10 By the Deficiency
11 Specific and General
12 The Remainders by the Last Digit
13 The Ultimate and Twice the Penultimate
14 By One Less than the One Before
15 The Product of the Sum
16 All the Multipliers


Note: The current Shankaracharya of Puri, Jagadguru Swami Nishchalananda Saraswati, has said (in 2008) he will be able to locate all the above sutras in the Vedic texts, but has so far only found one.

See also the article "The Sutras of Vedic Mathematics", by Kenneth Williams, published in the Journal of the Oriental Institute.

The Sub Sutras


  Sub Sutra Translation
 1  Proportionately
 2  The Remainder Remains Constant
 3  The First by the First and the Last by the Last
 4  For 7 the Multiplicand is 143
 5  By Osculation
 6  Lessen by the Deficiency
 7  Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency
 8  Last Totalling 10
 9  Only the Last Terms
10 The Sum of the Products
11 By Alternate Elimination and Retention
12 By Mere Observation
13   The Product of the Sum is the Sum of the Products
14 On the Flag


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