It was a summer vacation time, and then I was a high school student. I came across an unusual book. It said “you can do arithmetic’s at stunning speed without pen and paper” . I began to read the book and felt the magic .it was amazing, I was able to do arithmetic at stunning speed and the reason the Vedic mathematics .so there I began a journey to learn the deep secrets.
Basically Vedic arithmetic is all about applying some of the well established facts. Most of the people use calculators and they never bother to multiply say 48* 58 mentally .Experienced Engineers often do estimations just within seconds say calculating the floor area of multistory building .What enables them to do high speed math without calculator and even without a paper and Pen. The Answer is simple -experience, once your brain get familiar with a process eventually it’s trivial .Vedic Mathematics can give you an edge over others in doing arithmetic .remarkable change is observed in people who were trained in Vedic math’s .Actually Vedic math makes use of simple mathematical theorems .The Vedic mathematics was invented by Jagadguru Swami Bharati Krishna Tirthaji.He actually compiled all other those fundamental theorems called Sutras of Vedic math.
One Arithmetic operation that requires special attention is multiplication .Vedic math tricks can enable you to calculate the results within fraction of a second. Here I will illustrate technique, suppose you want to multiply some two digit decimal numbers Say 49*87
The calculation will be done as follows
49 *
87
(4*8)|(9*8+4*7)|(9*7)
32|100|63
32 |100| 3
32+10| 6|3
42|6|3
4263
Generalizing
AB*
CD
A*C|(A*D)+(B*C)|B*D
A Special Case is Squaring,
ie, A=C and B=D
ie AB*
A*A|2*A*B|B*B
An Acute observer would have already deduced the trick, it’s actually the polynomial multiplication, we are just manipulating the arrangement to produce the result and it implies higher power could also be implemented such as cube .Incase of rising to an integer power the general case becomes the terms of a binomial expansion. So this scheme can be extended to higher powers without any difficulty .moreover the operations involved can be generalized for N digits.(N+1) multiplications of order (N/2) digits and almost (N+1) additions can give the result of an N by N digit multiplications .Of course there are certain disadvantages .the Primary advantage is that it is suited for producing fixed precision arithmetic .Higher integer powers can be computed without any loss in precision .if a system can represent a N digit number then we can compute the product of N*N digit in N+1 Operations because N+1 multiplications are independent and N additions at most which may require result from previous stage. This result has great significance, arbitrary precision arithmetic can be implemented without any loss of information .On Contrary if we use Floating point multiplication there will be some loss of digits at very large values since the floating point actually compress the real range in exponential manner. Author is currently planning to develop integer math core in HDL languages.
Thus Vedic Math provides a convenient form of expression for arithmetic and author firmly believes that the sutras are manipulations of the well established mathematical theorems
So the Vedic mathematics ,particularly this technique enables us to calculate arithmetic in a single line .that’s this form is absolutely suited for array representation .More generally a matrix representation since long arrays can be represented as matrix by a simple indexing trick. There are about 16 ‘Sutras’ .the Above Sutra is “Vertically and crosswise” and is considered as the most general among the multiplication sutras.
Basically Vedic arithmetic is all about applying some of the well established facts. Most of the people use calculators and they never bother to multiply say 48* 58 mentally .Experienced Engineers often do estimations just within seconds say calculating the floor area of multistory building .What enables them to do high speed math without calculator and even without a paper and Pen. The Answer is simple -experience, once your brain get familiar with a process eventually it’s trivial .Vedic Mathematics can give you an edge over others in doing arithmetic .remarkable change is observed in people who were trained in Vedic math’s .Actually Vedic math makes use of simple mathematical theorems .The Vedic mathematics was invented by Jagadguru Swami Bharati Krishna Tirthaji.He actually compiled all other those fundamental theorems called Sutras of Vedic math.
One Arithmetic operation that requires special attention is multiplication .Vedic math tricks can enable you to calculate the results within fraction of a second. Here I will illustrate technique, suppose you want to multiply some two digit decimal numbers Say 49*87
The calculation will be done as follows
49 *
87
(4*8)|(9*8+4*7)|(9*7)
32|100|63
32 |100| 3
32+10| 6|3
42|6|3
4263
Generalizing
AB*
CD
A*C|(A*D)+(B*C)|B*D
A Special Case is Squaring,
ie, A=C and B=D
ie AB*
A*A|2*A*B|B*B
An Acute observer would have already deduced the trick, it’s actually the polynomial multiplication, we are just manipulating the arrangement to produce the result and it implies higher power could also be implemented such as cube .Incase of rising to an integer power the general case becomes the terms of a binomial expansion. So this scheme can be extended to higher powers without any difficulty .moreover the operations involved can be generalized for N digits.(N+1) multiplications of order (N/2) digits and almost (N+1) additions can give the result of an N by N digit multiplications .Of course there are certain disadvantages .the Primary advantage is that it is suited for producing fixed precision arithmetic .Higher integer powers can be computed without any loss in precision .if a system can represent a N digit number then we can compute the product of N*N digit in N+1 Operations because N+1 multiplications are independent and N additions at most which may require result from previous stage. This result has great significance, arbitrary precision arithmetic can be implemented without any loss of information .On Contrary if we use Floating point multiplication there will be some loss of digits at very large values since the floating point actually compress the real range in exponential manner. Author is currently planning to develop integer math core in HDL languages.
Thus Vedic Math provides a convenient form of expression for arithmetic and author firmly believes that the sutras are manipulations of the well established mathematical theorems
So the Vedic mathematics ,particularly this technique enables us to calculate arithmetic in a single line .that’s this form is absolutely suited for array representation .More generally a matrix representation since long arrays can be represented as matrix by a simple indexing trick. There are about 16 ‘Sutras’ .the Above Sutra is “Vertically and crosswise” and is considered as the most general among the multiplication sutras.
