What would 873 x 982 look like? Lots of lines. But still intriguing. Thanks Allison for sending this our way. Feel free to suggest a good link here...
in Math | December 13th, 2010 17 Comments
What would 873 x 982 look like? Lots of lines. But still intriguing. Thanks Allison for sending this our way. Feel free to suggest a good link here...
by Dan Colman | Permalink | Comments (17) |
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My Japanese wife says she has never seen such a way of multiplying. But very interesting anyway!
Vedic Maths! :-)
Yeah apparently it’s not Japanese, but Vedic.. check out this wikipedia article: http://en.wikipedia.org/wiki/Vedic_mathematics
This is really no different from multiplying the way we (westerners) do it with digits: multiply each digit in one number by each digit in the other, and carry over as needed. It seems to be a bit faster our way, especially for multi-digit multiplication, because you don’t have to draw all those lines.
Actually, it’s not really multi-digit multiplication that is a pain to do this way (with lines), it’s high-digit multiplication. Try multiplying 89 x 78 using lines, and you’ll quickly go back to multiplying the way you were taught.
This is not a Japanese means of teaching multiplication, but Vedic.
This method is ok for small numbers such from 1 to 5 but for 6,7… it is tedious to work out but this method of multiplicaion is suitable to teach for kids so that don’t get out of maths
Don’t be silly, Doctor.
It’s not the lines that make this easier and faster, it’s the orientation of the multiplicands, the order that you do the multiplication and adding.
In the western way, you make a large intermediate answer for every place in your multiplicand. So for 193×16, you get the answers for 193×6 and 193×10 before you get anything.
The flaw in this is that you’re always going to be adding the result of every one place digit by another one place digit, ten place multiplied by a one place together, then adding every ten by ten and hundred by one together and so on, but instead of performing *those* operations relevant to the final answer, we make a series of intermediate answers that are spaced with place holding zeros. When you’re doing a three digit number by a three digit number, the amount of added steps is really slow and cumbersome, and except for the first operation, these intermediate answers don’t give you any of the digits in the answer.
In this version, the vedic version, regardless of whether or not you draw any lines, you get the answers for each place digit individually.
So, typical western way goes like this: multiply, carry, add, carry, get the answer.
The vedic way, you multiply, add, carry, and then you have a digit from the answer. Each intermediate answer is simply another digit of your final answer, not a strange large number that serves merely as an opportunity to make a mistake. The third time I tried the vedic way, I got an answer pretty quickly, then I checked my work using the way I’d grown up with, and the answers didn’t match. I used a calculator–the vedic way was correct, the western way had several mistakes, even though I took longer to do it.
Brilliant. I think that this is a lot faster than long multiplication for 3 or 4 digit numbers. As long as you draw it at the correct angle and carry the tens over correctly there are no mistakes. Really great!!
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The kids at the school where. I worked did their homework so they could find where it would fail.
It’s nice, but it’s obvious it’s not faster than “Western” multiplication”.
well here is the thing. math is math is math. you can make proofs of different concepts in many ways due to the nature of math. myself, i help my daughter with her school work and she is just now learning multiplication, shes in 2nd grade. one of the techniques i taught her was the finger trick when multiplying numbers 1-9 by 9. i also showed her some other tricks. anyway when i saw this Japanese/Vedic way i couldn’t believe it. LOL I looked in to how it works with larger numbers like 1234X1232 etc… and it works. so i emailed her teacher with the link saying that I think that it is a technique that should supplement the times table. the reason is easy. when i was learning my times table it was a slow process. you don’t just learn them all right away. it takes practice. So, with this technique kids can use it as a proof of correctness while they are learning their times table. All kids have to do is know how to add. ITS GREAT!! when i saw this i felt stupid for not knowing this technique…lol and i pretty much minored in math. lol anyway that’s that on that..lol
This is the same way I was taught to multiply polynomials. For two digits we called it FOIL (first outer inner last). 21×13= (2x+1)*(x+3)=2x^2+(1+6)x+3 where x=10. The only difference is the visualization.
1. THE NUMBER SYSTEM
The decimal number system and the place value system in use today was first recorded in Indian mathematics.
2. THE ZERO
Indian mathematicians made early contributions to the study of the concept of zero as a number.the ancient romans did not know the number o but the Indians had the knowledge of large numbers like mahogham(1 followed by 62 zeros) and It was the indain mathematician Aryabhatta who invented 0 . without 0 there would be no binary system and no computer: counting would be clumsy and cumbersome.
3. THE GRADUATED CALCULATION
This method of graduated calculation was documented in the Pancha-Siddhantika (Five Principles) in the 5th Century But the technique is said to be dating from Vedic times circa 2000 B.C
4. VALUE OF PI
The value of pi was first calculated by Budhayana, & he explained the concept of what is now known as the Pythagorean Theorem. British scholars have last year (1999) officially published that Budhayan’s works date back to the 6th Century, which is long before the European mathematicians
5. ALGEBRA
In ancient India conventional mathematics termed Ganitam was known before the development of algebra. This is borne out by the name – Bijaganitam, which was given to the algebraic form of computation the inference that Bijaganitam was the original form of computation is derived.
6. GEOMETRY
Even in the area of Geometry, Indian mathematicians had their contribution. There was an area of mathematical applications called Rekha Ganita (Line Computation). The Sulva Sutras, which literally mean ‘Rule of the Chord’ give geometrical methods of constructing altars and temples.
7. CALCULUS
Calculus, an Indian invention, was picked up by the Jesuit priests from Kerala in the second half of the 16th century and taken to Europe. This is how the Westerners got their calculus.
8. PYTHAGORAS THEOREM
The famous Pythagoras theorem is explained several centuries before in the shulva sutras of the Vedas. It is believed that the much travelled Pythagoras was a student at the takshashila university in undivided india and he carried with him the knowledge of mathematics to the western world.
9. THE LARGEST NUMBER
The largest numbers the Greeks and the Romans used were 10**6(10 to the power of 6)
Hindus used numbers as big as 10**53(10 to the power of 53) with specific names as early as 5000 BCE during the Vedic period
Even today, the largest used number is Tera 10**12(10 to the power of 12)
10 Binary System and Hashing Algorithms are also invented in india thousands of years before.
Forgot to mention Vedic Maths has lots of shortcuts for calculating large numbers.
Also forgot Concept of Infinity in maths is also Originated in india.
Vedas and Upnishad are ocean of knowledge (Science, Maths, Philosophy, etc.)