VEDIC MATHS-105

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 105 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Applications of the Sutras & Sub-sutras - 5"

VEDIC MATHEMATIC :

"VEDIC MATHEMATICS" is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles, with which any mathematical problem be it arithmetic, algebra, geometry or trigonometry can be solved, hold your breath, orally!

What we call "Vedic Mathematics" is a mathematical elaboration of 'Sixteen Simple Mathematical formulae from the Vedas' as brought out by Sri Bharati Krishna Tirthaji.

Sutras: 

The system is based on 16 Vedic sutras or aphorisms, which are actually word formulae describing natural ways of solving a whole range of problems.

Some examples of sutras are "By one more than the one before", "All from 9 & the last from 10", and "Vertically & Crosswise". These 16 one-line formulae originally written in Sanskrit, which can be easily memorized, enables one to solve long mathematical problems quickly.

9. Chalana – Kalanabhyam ( Differences and Similarities )

i. In the first instance, it is used to find the roots of a quadratic equation 7×2 – 11x – 7 = 0. Swamiji called the sutra as calculus formula. Its application at that point is as follows. Now by calculus formula, we say: 14x–11 = ±√317

A Note follows saying every Quadratic can thus be broken down into two binomial factors. An explanation in terms of the first differential, discriminant with a sufficient number of examples are given in the chapter ‘Quadratic Equations’.

ii. In the Second instance under the chapter ‘Factorization and Differential Calculus’ for factorizing expressions of 3rd, 4th and 5th degree, the procedure is mentioned as ‘Vedic Sutras relating to Chalana – Kalana – Differential Calculus’.

Further other Sutras 10 to 16 mentioned below are also used to get the required results. Hence the sutra and its various applications will be taken up at a later stage for the discussion.

( For  more information refer -: VEDIC MATHS-96 )

10. Ekanyunena Purvena ( By one less than the previous one ) 

For multiples of 9 as a multiplier, the first digit is 1 less than the first digit of the multiplicand and the second digit is subtracting the lessened digit from multiple of 9.

Examples:

1. 5 x 9  = 45
    5-1= 4,   9-4 = 5

2. 14 x 99 = 1386
    14-1=13, 99-13 = 86

For multiplier less than the multiplicand, the first digit is an additional 1 of the first digit of the multiplicand less than the latter and the second digit is subtracting the second digit of the multiplicand by 10.

Examples:

3. 12 x 9 = 108 
    12-2 = 10, 10-2 = 8

4. 28 x 9 = 252
    28-3 = 25, (10-8) = 2

( For  more information refer -: VEDIC MATHS-4 )

In next blog we will discuss about "Applications of the Sutras & Sub-sutras - 6".     

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