By Rupali Patil
October 1998
The ancient science of Vedic mathematics may well give calculators a run for their money
Does your mind wobble when confronted by a mathematical challenge more forbidding than two plus two? Do you dream of becoming the kind of person who can rattle off answers to the most complicated sums in the fraction of a second? If the answer is yes, you need Vedic mathematics. Try this for size. What’s the square of 65? Simple: just multiply the first digit, 6, with its successor, 7. The answer is 42. Now find the square of the second digit, five, which is 25. Now bring the two together. Bingo, the answer is 4225! Don’t believe it? Try it out with any two digit odd number divisible by five.
The law behind this apparent magic is the nikhilam sutra, one of the sutras or formulae that compose Vedic mathematics. These sutras were part of the parisista (appendix) of the Atharva Veda. ‘Our Vedas are the original source of knowledge. Vedic mathematics,’ says Dr Narendra Chaudhury, ‘is one such source.’ A geology professor at Nagpur University in western India, Chaudhury turned to Vedic mathematics after attending a conference organized by the Einstein Foundation in 1984. Introduction to Vedic mathematics is like entering Alice’s wonderland, where logic is turned on its head. Division is by a process of multiplication and addition, and multiplication is done by cross-subtraction. Nothing makes sense, but everything works. And the simplicity of the approach exposes top-heavy processes of our logic-driven world.
Unlike conventional mathematics, Vedic mathematics is not linear. Here, it would be as easy to multiply 432567 with 754352 as it would be to multiply four into five. This is because the processes are governed by an internal relationship between numbers rather than by external methods of conventional mathematics. Another distinguishing characteristic ofVedic mathematics is its holistic approach. Numbers are not separated from their philosophical and spiritual contexts. Number one stands for the Absolute, and therefore it cannot be subtracted or divided. Two represents unmanifest nature and three manifest nature. Four is associated with the world of mind and feeling. Number five represents ether and has the quality of sound. Six is air and possesses the quality of touch. Fire is at seven and water at eight. Finally, nine is represented by earth. Such an intimate relationship between numbers and the elements of the universe creates a unified body of knowledge that is far easier to follow than the fragmentary western way. To keep things simple, Vedic mathematics constantly reiterates that there are only nine numbers and a nought, and everything else derives from these.
Vedic mathematics, as it is found today, was formulated by the late Bharti Kishan Tirthaji, the Shankaracharya of Puri, a seaside temple town in the eastern Indian state of Orissa. He introduced 32 sutras through a study of the ancient texts, coupled with an insight into the nature of numbers. There are 16 main sutras and 16 sub-sutras. Application of the sutras depends on the problem: Vedic mathematics provides more than a way of solving a problem-the easiest is the best. Chaudhury rues the general ignorance shrouding Vedic mathematics. ‘The main reason,’ he says, ‘is the low awareness and the lack of an efficient faculty. Nobody will appreciate it unless the topic is made interesting.’ To make Vedicmathematics more accessible, it is necessary for the subject to be included in school curricula. Making learning fun is an oft-voiced concern. The means lie in ancient wisdom—which is ours to use or throw!
Addition
6932+1803+3331=12066
This can be cross-checked in the following manner:
i) 6+9+3+2=20=2(2+0)
ii) 1+8+0+3=12=3(1+2)
iii) 3+3+3+1=10=1(1+0)
iv) 2+3+1=6
v) 1+2+0+6+6=15=6(1+5)
Steps (iv) and (v) contain the same digit and that is 6. So the solution is accurate.
Vertical and Crosswise Multiplication
The conventional method of multiplying 24 into 36 would go like this:
24
x36
144
72-
864
The Vedic method will work out the sum thus:
24 is the multiplicand and 36 is the multiplier
Step 1: Vertical multiplication
Multiply the left-most of the multiplicand, in this case 2 24 with the leftmost digit of the multiplier, in this case 3 x36
So, 2×3=6 6
Step 2: Crosswise multiplication
Multiply the first digit of the multiplicand, in this case 2 with the second digit of the multiplier, in this case 6 So, 2×6=12
Now, multiply the second digit of the multiplicand, in this case 4 with the first digit of the multiplier, in this case 3 So, 4×3=12
Add the two products: 12+12 =24 24 Place the second digit of the total next to the result of x36 step 1 and carry 2 to the next line 64 2
Step 3: Vertical multiplication
Multiply the right-hand digits multiplicand and 24 multiplier. 4×6=24 x 36 Place 4 at the right hand most of the answer 644 and carry 2 to the next line + 22 Final result: 864
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