Introduction:

This page has been created after some interesting feedbacks from folks, for my postings in India Discussion digest on Vedic Mathematics.

Vedic Mathematics is a form of mathematics that has been there in India from pre-historic times. Many saints and others (including Shankaracharyas) have contributed to this amazing mathematical idea, which is basically a large set of algorithms, so to speak, for simple and complex computations. There may be more than that in Vedic Mathematics, I am a novice in the field. These simple techniques is just one proof to show how much people have used their brain, when there was no pencil and paper (and of course calculator!). No wonder, great epics and other things have stood for centuries.

I am giving a few examples that I posted recently in the discussion digest, and will update it, whenever I find time. Readers of this site, feel free to email me your ideas, examples, pointers like books, I shall post them in this site.

Some examples in Vedic Mathematics:

This section contains examples posted by me and others recently (June 1997) in IDD as is(Let me know if there are any critical typos). As I said, feel free to email me more stuff.

1. If you want to multiply any number with 9, 99, 999,...just use this rule: eg. 999x343=342657 (second number -1)(subtract 9 from each of these new digits)ie. 342 and (9-3)(9-4)(9-2)

2. If you want to square a number that is closer to 10, 100, 1000, ...: eg. 988^2=976144 (base number-(nearest '0' number - the base number))(square of the inner difference) ie. 988-(1000-988)and(1000-988)^2. I am at loss of words here, hope you get the idea.

3. If you want to square a number (that is not closer to 10, 1000,...): eg. 43^2=1849 (first digit x (the base number + second digit))(square of second digit) ie. (4 x (46))(3^2)=>1849

4. The square of any number ending in a five: (x5)^2 = [(x)(x+1)]25 Examples: 15^2 = ((1)(1+1))25 = 225 95^2 = (9(9+1))25 = 9025

5. The result of one over any number ending in a 9 can be computed in two very simple ways. I will give the easier example. 1/x9 ->

a. Take the digit x. Increment it by one.

b. Start with a 1 one on the left.

c. Multiply that number by (x+1) and write that number to the left of it.

d. Now take this new number. Multiply this number by (x+1).

e. Write the last digit of the result to the left of the result so far.

f. Any carry over, remember it.

g. Take the last digit of result entered. Multiply it with (x+1) and add the carry over remembered in step f.

h. Write the last digit of the result to the left of the result so far.

i. Any carry over, remember it.

j. Repeat the steps g, h, and i untill the result pattern starts repeating or you hit a zero as the result digit..

k. In most cases the pattern will repeat after every (x9 - 1) digits of result.

6. Here are examples, again for numbers closer to 10, 100, 1000... If you want to multiply two of these numbers, here are two cases: (Since folks are getting confused with syntax, I am just giving examples)

a. 95 x 97 = <97-(100-95)><(100-95)x(100-97)> = <92><5x3> = 9215 It is actually much easier when you write it on a piexe of paper.

b. if one of the numbers is over the '0' number: 94 x 104 = <104-(100-94)><(100-94)x(100-104)>. Here is where you use your intuition. The next step is (9800)-(24)=9776

This logic above cannot be used for numbers that are not close to 10, 100,1000 etc.

<<Look here for more additions>>

Sources for more learning:

(Disclaimer - I have no connecion with any of the following sources)

1. A good Vedic Mathemtics site : http://www.silverleaf.com/jiva/observe/vedicmat/vedicmat.html

2. Origin of VM : http://www.silverleaf.com/jiva/observe/vedicmat/orgnstra.html

3. Book on VM : http://www.silverleaf.com/jiva/observe/vedicmat/isbnetc.html

4. More VM : http://gupta.cs.uiuc.edu/~rgupta/vedic.html