The essence of Vedic mathematics.

MSN Group ^ | n/a | Rupali Patil

[sere]

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.

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http://groups.msn.com/magicalmethods/general.msnw?action=get_message&mview=1&ID_Message=301

[Talking_Mouse]

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[georgiadevildog]

From one math nerd to another: thanks! My mother the math teacher will surely love this one. Incidentally, ever use the "bridge" method to do the 11-19 times tables?

[Eepsy]

I think they must mean any two digit number /ending/ in five, not divisible. To find the square of any two digit number ending in zero, you simply square the first digit and add two zeros.

[Eepsy]

Ooo, I've not heard of that one. Do tell!

[laredo44]

I think they must mean any two digit number /ending/ in five, not divisible.

They said any two-digit odd number divisible by 5, which of course is the same as any two digit number ending in 5.

[CurlyDave]

The only odd two digit numbers divisible by 5 end in 5.

[Nick Danger]

Looks like a re-hash of Tractenberg.

[Eepsy]

Doh!

[texas booster]

In Texas we have a school competition called Number Sense. 80 problems, from arithmetic to calculus, 10 minutes to solve, no calculators or scratch paper.

I did fairly well for a kid who never had a class above HS geometry. The tricks I learned to compute simple math made me seem like a genius to others.

Kids who were good at it could solve all 80 problems with no mistakes in about 9 minutes.

[beef]

ping

[georgiadevildog]

I'd love to see/take that test!

[megatherium]

The Indians do have much to be proud of in terms of mathematics: they originated our base 10 number system (which we call Arabic, but the Arabs got it from India). They were very good at number theory and geometry. Forgive the following technical detail, but Indian mathematicians discovered power series for trigonometric functions before Western mathematicians. And many people are familiar with the amazing story of the early 20th century mathematician Ramanujan.

But allow me to say that this "Vedic mathematics" looks like a bunch of mystic mumbo-jumbo wrapped up in a collection of clever number tricks. I don't doubt the tricks work, and it might be fun to learn them, but someone with a serious interest in math would be much better off learning "western mathematics" (that actually the whole world now holds in common, from east Asia to the USA). If you've had university math through calculus, try to find a good intro number theory text. Many lovely theorems about numbers to amaze you. (If you haven't had calculus, but are very good at algebra, you might find an elementary number theory text that's accessible to you.)

[boojumsnark]

And many people are familiar with the amazing story of the early 20th century mathematician Ramanujan.

Many people are familiar with the story; very, very few (certainly not I) can grasp the beauty and depth of what he did. Tragically, Ramanujan died too early.

Same thing with Galois, but he was French. Read HIS story!

[megatherium]

There is the striking quote by the English mathematician G. H. Hardy. He received a letter, out of the blue, from Ramanujan (who was unknown and impoverished), saying that he had been working on some mathematics. The letter gave some extraordinary number-theoretic formulas. Hardy knew at once that this wasn't a hoax or joke, because no one would have had the imagination necessary to dream up such formulas if they weren't real. In the event, nearly all of the formulas proved correct. Anyway, what Hardy said was that this was the only genuinely romantic episode in his life. ("Romantic" in the older sense, as Merriam Webster defines the word: marked by the imaginative or emotional appeal of what is heroic, adventurous, remote, mysterious, or idealized.)

Evariste Galois is one of the true tragedies of mathematics. The romantic version of the story is that he frantically wrote down his mathematical discoveries the night before his certain death in a duel with one of France's best duellists. Indeed, he died at 21 in this duel. It isn't clear what the duel was over: a woman, or politics. The truth is that Galois had already detailed his work months earlier in a manuscript he had already sent to the best French mathematicians. "Galois theory" is still the subject of active research in modern mathematics.

Another tragic early death in mathematics was that of the Norwegian mathematician Niels Abel, who made several spectacular discoveries (some related to the math Galois also worked on) before his death at 26 of tuberculosis. Abel died in 1827; Galois in 1832.

If any of this interests anyone, there's a marvelous web site: The MacTutor History of Mathematics Archive

[valkyrieanne]

But allow me to say that this "Vedic mathematics" looks like a bunch of mystic mumbo-jumbo wrapped up in a collection of clever number tricks. I don't doubt the tricks work, and it might be fun to learn them, but someone with a serious interest in math would be much better off learning "western mathematics"...

Yes, however, the Vedic math techniques made it possible for people *without calculators* to do math very quickly in their heads. In their era it was far more significant than it would be for us today.

[ArrogantBustard]

I think they must mean any two digit number /ending/ in five, not divisible.

They specify "odd number" divisible by five ... all of which, of course, end with the digit "5" ...

[megatherium]

In their era it was far more significant than it would be for us today.

The big innovation in western mathematics, which dramatically simplified arithmetic for scientific calculations, was logarithms (in the early 1600s). These were invented by John Napier. This greatly speeded multiplication, division, powers and roots. For example: to find the cube root of 343, you look up the common log; it's 2.5353 (rounded to 4 decimals). Then you divide that by 3. You get 0.8451. You look in your log table for the number with log 0.8451. You find 7.0000.

At some time soon thereafter, slide rules were invented. These are essentially log tables on a stick. I have my late grandfather's fine Keuffel and Esser slipstick. I figure if nuclear electromagnetic pulse ever happens, and all electronic computational devices are fried, I'll be in very good shape.

Of course, logs aren't so useful for checkbook calculations. Fast mental arithmetic tricks might be very handy for that. But sophisticated finance calculations would still need logs galore.

Napier, by the way, was famous in his lifetime for writing a best-selling book that claimed that the Pope was the antichrist, and the end of the world would happen in 1786.

[Calusa]

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[sere]

""The uses of Vedic Mathematics are very broad. Sixteen Sutras and thirteen Sub-Sutras can be applied to all walks of mathematics. Research shows its application in Fast Calculations (multiplication, division, Squaring, Cubing, Square Root, Cube Root), trigonometry, three-dimensional coordinate geometry, solution of plane and spherical triangles, linear and non-linear differential equations, matrices and determinants, log and exponential. The most interesting point is to note that the Vedic Mathematics provides unique solutions in several instances where trial and error method is available at present."

It becomes more usable in preparing for competitive exams when there is not enough time to attempt all questions.