Vedic Mathematics

Superb how these ancients knew about maths and science.

About Vedic Mathematics

Did you know if you if you want to find the square of 45, you can employ the Ekadhikena Purvena sutra ("By one more than the one before"). The rule says since the first digit is 4 and the second one is 5, you will first have to multiply 4 (4 +1), that is 4 X 5, which is equal to 20 and then multiply 5 with 5, which is 25. Viola! The answer is 2025. Now, you can employ this method to multiply all numbers ending with 5.


If you want to subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321. Similarly, other sutras lay down such simple rules of calculation.

Did you know a man by the name of Madhava, identified the expansion of cos and sine functions almost three centuries before Newton!

Indian Maths
Indic Mathematics

Madhava (14th C, Kochi) made important mathematical discoveries that would not be identified by European mathematicians till at least two centuries later. His series expansion of the cos and sine functions anticipated Newton by almost three centuries. Nilkantha (15th C, Tirur, Kerala) extended and elaborated upon the results of Madhava while Jyesthadeva (16th C, Kerala) provided detailed proofs of the theorems and derivations of the rules contained in the works of Madhava and Nilkantha. It is also notable that Jyesthadeva's Yuktibhasa which contained commentaries on Nilkantha's Tantrasamgraha included elaborations on planetary theory later adopted by Tycho Brahe, and mathematics that anticipated work by later Europeans.

Chitrabhanu (16th C, Kerala) gave integer solutions to twenty-one types of systems of two algebraic equations, using both algebraic and geometric methods in developing his results. Important discoveries by the Kerala mathematicians included the Newton-Gauss interpolation formula,the formula for the sum of an infinite series, and a series notation for pi.

Charles Whish (1835, published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland) was one of the first Westerners to recognize that the Kerala school had anticipated by almost 300 years many European developments in the field.

Thanks for all the information, aryaputhra. It makes me feel proud to be an Indian.

A lot of people didn't use to give enough credit to the original founders of the basic mathematical concepts.

"The study of mathematics in the West has long been characterized by a certain ethnocentric bias, a bias which most often manifests not in explicit racism, but in a tendency toward undermining or eliding the real contributions made by non-Western civilizations. The debt owed by the West to other civilizations, and to India in particular, go back to the earliest epoch of the "Western" scientific tradition, the age of the classical Greeks, and continued up until the dawn of the modern era, the renaissance, when Europe was awakening from its dark ages. This awakening was in part made possible by the rediscovery of mathematics and other sciences and technologies through the medium of the Arabs, who transmitted to Europe both their own lost heritage as well as the advanced mathematical traditions formulated in India." - Dr. David Gray.

"The world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension."
~ A.L. Basham, Australian Indologist in The Wonder That Was India

"India was the motherland of our race and Sanskrit the mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity...of self-government and democracy. In many ways, Mother India is the mother of us all."
~ Will Durant, American Historian 1885-1981

Originally posted by aryaputhra
Superb how these ancients knew about maths and science.

About Vedic Mathematics

Did you know if you if you want to find the square of 45, you can employ the Ekadhikena Purvena sutra ("By one more than the one before"). The rule says since the first digit is 4 and the second one is 5, you will first have to multiply 4 (4 +1), that is 4 X 5, which is equal to 20 and then multiply 5 with 5, which is 25. Viola! The answer is 2025. Now, you can employ this method to multiply all numbers ending with 5.

Interesting, and the people that composed these lines had this in mind?

Did they also invent sophistry?

If you want to subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321. Similarly, other sutras lay down such simple rules of calculation.

Those are hardly rules of calculation. They're lines from a text that could be made to get at a particluar number solution.

The rest was intersting tho. Those clever malyalis!

While I believe ancient Indian mathematics was very advanced, I would have to question this "vedic mathematics" it seems like most of the creative genius behind vedic mathematics, is not from ancient India, but from the person who invented it, or supposedly, reintroduced it.

A line such "all from 9 last from 10" and the subsequent calculation methods, just don't seem to correlate. It seems more like wishful thinking to me on part of the creator of the system. The author claimed that any mathematical can be done, with simple, one step mental arithmetic, is also not true.

Even employing the systems of vedic mathematics, I could not do it one simple mental step. I also found a lot of the math too be too "high school" level. It's pretty good for party tricks or impressing people, but it's not very practical for serious mathematicians.

I really don't understand why you find it so difficult? The first thing that has to happen is throw all the western methods of calculation out of the window. Otherwise you will need a calculator when it comes to big numbers. I recall my uncle who used vedic methods to calculate and balance his books.

The principle of Nikhilam Navatas'caramam Dasatah ("all from 9 and the last from 10") is very simple and easy to learn.

Take for example simple numbers

7 (N1). -> The nearest base of 7 is 10. (Deviations are arived from the nearest base)

8 (N2). -> The nearest base of 8 is also 10.

The deviation from base of 7 is -3 (7-10). Call this D1.
The deviation from base of 8 is -2 (8-10). Call this D2.

Step 1:
N1 + D2 = 7 - 2 = 5
or
N2 + D1 = 8 - 3 = 5

Step 2:
The multiplication of the two bases (D1 X D2); 3 X 2 = 6.

Step 3
Now to get to the multiplication result of 7 X 8, take result of Step 1 (5) together with the result of step 2 (6), which gives you 56!

Similarly;

994 X 988. Base is 1000.

Step 1.
N1 + D2 = 994 - 012 = 982
or
N2 + D1 = 988 - 006 = 982

Step 2.
N1 = 994 - 1000 = -006
N2 = 988 - 1000 = -012

006 X 012 = 072 (this vedic maths, zeroes are important. :cool.

Step 3
Take result of Step 1 (982) together with the result of step 2 (072), which gives you 982072!

What's so difficult? Granted some of the other sutras can be mind boggling but certainly not the "all from 9 and the last from 10" rule. You really need to grasp Vedic maths from the roots not halfway with the current mathematic systems in place. Then, you will be running for the calculators.

And I don't believe one person came up with all these intepretations! If so, we would need to find him/her/it and give him a nobel prize!!

more here.



[edit on 20-10-2004 by aryaputhra]

Vedic maths eh? [/ Hmmmm very interesting (said in a kind of german scientist way)

Seriously though its never surprising to see blatant displays of culture and science when the civilization in question is a few thousand years older than ours.

Originally posted by aryaputhra

Well exactly Aryaputhra, the system involves some mathematical tricks, that can be done on certain numbers. The difficult part, is remembering all the tricks, and then doing them in your head. For instance, even after you applied the vedic method, we still had to multiply 12 by 6. Which is farily easy, but many would also have problems. In the end you are still using the western method: (6*10) + (6*2)

What if you had a harder calculation like: 982072 * 45262. Can you do that in your head with a single step vedic technique? I doubt it.

[edit on 21-10-2004 by Indigo_Child]