Math + Vishnu = Really Fast Math
May 28, 2007 12:12 AM Subscribe
What is the square of 85? In an instant, a 17-year-old boy said without blinking, "7,225." Kamlesh Shetty had used a trick from a quaint concept called Vedic math, a compilation of arithmetic shortcuts believed to have been written by ancient Indians who lived centuries before Christ, during a glorious period in Indian history called the Vedic Age. More on Vedic math. Still more. And there's a similar system called the Trachtenberg system, invented in a Nazi concentration camp. Where were these guys when I was in the third grade struggling with my times tables?
I had been wondering about mathematical shortcuts and why they worked, and wanted to post an AskMe question to see if anyone had any tips on shortcuts like my math teachers did, such as "any number whose sum of digits is divisible by 3 is divisible by 3", or the SOHCAHTOA mnemonic for trigonometry. I had no idea there were entire systems for this. Thanks!
posted by Lush at 12:26 AM on May 28, 2007
posted by Lush at 12:26 AM on May 28, 2007
IIRC according to Feynman the smart people at Los Alamos also entertained themselves with math puzzles like this. 85 x 85 is (100-15)*(100-15), which, if we remember our algebra is a2-2ab+b2, or 10,000 - 3,000 + 15x15.
Basically, for the mathematically literate, the numerical landscape is strewn with hacks and shortcuts.
posted by Heywood Mogroot at 12:38 AM on May 28, 2007
Basically, for the mathematically literate, the numerical landscape is strewn with hacks and shortcuts.
posted by Heywood Mogroot at 12:38 AM on May 28, 2007
85 x 85 is (100-15)*(100-15), which, if we remember our algebra is a2-2ab+b2, or 10,000 - 3,000 + 15x15.
I suppose this is OK for those slackers who've forgotten their 85 times tables.
posted by thatwhichfalls at 12:48 AM on May 28, 2007 [8 favorites]
I suppose this is OK for those slackers who've forgotten their 85 times tables.
posted by thatwhichfalls at 12:48 AM on May 28, 2007 [8 favorites]
That's not math, that's arithmetic. It's not 'Vedic', it's most likely from a Vedanga, most likely Vedanga Jyotisa or later related treatises such as Bhaskaracharya's Leelavati Ganitam.
In fact, I remember skimming through this Swami's book many many years ago, and was immediately struck by a complete absence of citations and such; the Vedas have a very complex system of identifying exact sutras and such. I was also struck by the close resemblance between long-form multiplication methods mentioned here and in the Leelavati gaNitam, which I happened to be researching at about that time for a different reason.
In short, pending clear citations and/or actual Sanskrit slokas that can be traced to the Atharva Veda, I would call shenigans. I'll even go as far as accusing the Swami of possibly plaigarising Bhaskaracharya.
There's a very good reason why easy math strategies were necessary. Computationally speaking, the Indic calendar system is the most complex in the world; if you were to compute all of the world's calendars using all their individual algorithms handed down by tradition, you'd find that you'd take the maximum time to compute the Indic calendar system. (This is very easily verifiable; there's already a world-calendars framework out there on the web which you could download and compile/run.)
That said, the Indian exam system didn't allow calculators as recently as 1999, so this was extremely useful. Which brings me to the second grudge on all this 'vedic math' branding:- computational speed is only a gimmick. The real value here is correctness; in the many years I used to multiply/divide using this system, I've very rarely had an error.
posted by the cydonian at 3:34 AM on May 28, 2007 [8 favorites]
In fact, I remember skimming through this Swami's book many many years ago, and was immediately struck by a complete absence of citations and such; the Vedas have a very complex system of identifying exact sutras and such. I was also struck by the close resemblance between long-form multiplication methods mentioned here and in the Leelavati gaNitam, which I happened to be researching at about that time for a different reason.
In short, pending clear citations and/or actual Sanskrit slokas that can be traced to the Atharva Veda, I would call shenigans. I'll even go as far as accusing the Swami of possibly plaigarising Bhaskaracharya.
There's a very good reason why easy math strategies were necessary. Computationally speaking, the Indic calendar system is the most complex in the world; if you were to compute all of the world's calendars using all their individual algorithms handed down by tradition, you'd find that you'd take the maximum time to compute the Indic calendar system. (This is very easily verifiable; there's already a world-calendars framework out there on the web which you could download and compile/run.)
That said, the Indian exam system didn't allow calculators as recently as 1999, so this was extremely useful. Which brings me to the second grudge on all this 'vedic math' branding:- computational speed is only a gimmick. The real value here is correctness; in the many years I used to multiply/divide using this system, I've very rarely had an error.
posted by the cydonian at 3:34 AM on May 28, 2007 [8 favorites]
Math is my weak side - but this was pretty interesting. Thanks!
posted by homodigitalis at 5:55 AM on May 28, 2007
posted by homodigitalis at 5:55 AM on May 28, 2007
85*85 = (80+5)*(90-5) = 80*90 + (90-80)*5 - 25 = 80*90 + 25.
65*65 = 70*60+25, etc...
posted by of strange foe at 6:25 AM on May 28, 2007
65*65 = 70*60+25, etc...
posted by of strange foe at 6:25 AM on May 28, 2007
I'd heard fellow mathematicians from India complaining about this fad, and indeed on first glance it doesn't look particularly impressive -- more like a big collection of tricks that give correct answers to a very limited selection of problems, without promoting any sort of systematic understanding of what's actually going on.
That said, I would certainly encourage my own kids to learn these tricks -- tricks are good!
posted by escabeche at 7:56 AM on May 28, 2007
That said, I would certainly encourage my own kids to learn these tricks -- tricks are good!
posted by escabeche at 7:56 AM on May 28, 2007
"That's not math, that's arithmetic. It's not 'Vedic', it's most likely from a Vedanga..."
Oof courrrse eweryvon knowz areethmehtik vas inwented by duh Russians!
posted by ZachsMind at 8:02 AM on May 28, 2007
Oof courrrse eweryvon knowz areethmehtik vas inwented by duh Russians!
posted by ZachsMind at 8:02 AM on May 28, 2007
The way I did it in my head:
1) 85 is 80 + 5.
2) 85 * 85 = (80 * 80) + (5 * 5) + 2 (80 * 5)
3) 6400 + 25 + 800
4) 7225
None of these individual steps is hard. 80 squared is 8 squared * 100, obviously, and 6400 + 800 is only hard if you don't know the trick to adding 8: decrement the ones digit by two and increment the tens digit.
It took me a couple of minutes and I had a false start, but that's because I'm way out of practice. If you devote serious time to it, like this kid probably did, then there is really no trick to this.
posted by JHarris at 11:42 AM on May 28, 2007
1) 85 is 80 + 5.
2) 85 * 85 = (80 * 80) + (5 * 5) + 2 (80 * 5)
3) 6400 + 25 + 800
4) 7225
None of these individual steps is hard. 80 squared is 8 squared * 100, obviously, and 6400 + 800 is only hard if you don't know the trick to adding 8: decrement the ones digit by two and increment the tens digit.
It took me a couple of minutes and I had a false start, but that's because I'm way out of practice. If you devote serious time to it, like this kid probably did, then there is really no trick to this.
posted by JHarris at 11:42 AM on May 28, 2007
I pulled one of these out on my 4th grade teacher (courtesy Square One), who subsequently became convinced I was a young prodigy and enrolled me in the gifted math program.
Television: cause of and solution to...
posted by Adam_S at 11:56 AM on May 28, 2007
Television: cause of and solution to...
posted by Adam_S at 11:56 AM on May 28, 2007
(10a+5)*(10a+5)=100a^2+100a+25
(10a+5)*(10a+5)=100(a^2+a)+25
(10a+5)*(10a+5)=100a(a+1)+25
In other words, take the number in front of the 5, multiply it by the next consecutive number, and tack 25 on the end.
8*9=72 85*85=7225
It's a trick that was taught me all the way back in 8th grade algebra. It's not rocket science.
posted by jonp72 at 12:54 PM on May 28, 2007 [1 favorite]
(10a+5)*(10a+5)=100(a^2+a)+25
(10a+5)*(10a+5)=100a(a+1)+25
In other words, take the number in front of the 5, multiply it by the next consecutive number, and tack 25 on the end.
8*9=72 85*85=7225
It's a trick that was taught me all the way back in 8th grade algebra. It's not rocket science.
posted by jonp72 at 12:54 PM on May 28, 2007 [1 favorite]
Personally, I just type Command-Space, =85*85, and tap enter. Quicksilver then gives me the answer.
Thus, I can put more important things into my head, like what to have for supper.
posted by five fresh fish at 1:37 PM on May 28, 2007 [2 favorites]
Thus, I can put more important things into my head, like what to have for supper.
posted by five fresh fish at 1:37 PM on May 28, 2007 [2 favorites]
Advertising as entertainment:
I was able to join the Apple "genius" in confounding the pc man by knowing the square root of 4096, and pi to 5 places.
I would have guessed the pc man was miffed at 20 on a scale of 1 to 10.
posted by Cranberry at 1:49 PM on May 28, 2007
I was able to join the Apple "genius" in confounding the pc man by knowing the square root of 4096, and pi to 5 places.
I would have guessed the pc man was miffed at 20 on a scale of 1 to 10.
posted by Cranberry at 1:49 PM on May 28, 2007
This is, like, the oldest math trick in the book. I can't believe this got any attention.
Hey kids, Sohcahtoa. And while you're at it, the derivative of sin x is cos x.
posted by Civil_Disobedient at 3:00 PM on May 28, 2007
Hey kids, Sohcahtoa. And while you're at it, the derivative of sin x is cos x.
posted by Civil_Disobedient at 3:00 PM on May 28, 2007
I watched a guy demonstrating this recently at the Mind, Body & Spirit Festival. It was very impressive so I went to his stall a little bit later to have a chat. He told me all about his guru and how he'd travelled the world lecturing and never received a penny, he just did it for the love. The guy at the festival obviously didn't want to follow in his footsteps. There were some books and DVDs for sale at the stall. He'd had them printed in India and the text was a little small but he wanted to get a lot of information in to what was quite a small volume. The prices started at US$40. Thank you for this post frogan. It's a good stepping off point for me.
posted by tellurian at 4:40 PM on May 28, 2007
posted by tellurian at 4:40 PM on May 28, 2007
That's not math, that's arithmetic.
Missed a day in set theory, apparently.
posted by DU at 5:27 PM on May 28, 2007
Missed a day in set theory, apparently.
posted by DU at 5:27 PM on May 28, 2007
Oof courrrse eweryvon knowz areethmehtik vas inwented by duh Russians!
In Soviet Russia, Nines cast out YOU.
posted by otherchaz at 5:48 PM on May 28, 2007 [2 favorites]
In Soviet Russia, Nines cast out YOU.
posted by otherchaz at 5:48 PM on May 28, 2007 [2 favorites]
in general:
the product of any two numbers such that; the higher order numbers are the same (x) and the units add up to ten (y and 10-y) = x*(x+1) *100 + (y*(10-y).
so it not only works for a square but also for 23*27 or 99*91 or even for 2003 *2007
posted by shnarg at 6:00 PM on May 28, 2007
the product of any two numbers such that; the higher order numbers are the same (x) and the units add up to ten (y and 10-y) = x*(x+1) *100 + (y*(10-y).
so it not only works for a square but also for 23*27 or 99*91 or even for 2003 *2007
posted by shnarg at 6:00 PM on May 28, 2007
Thanks.
This Vedic Math thing is going to come in really handy the next time I need to calculate the square of, say, 65 or 105.
posted by sour cream at 10:51 AM on May 29, 2007
This Vedic Math thing is going to come in really handy the next time I need to calculate the square of, say, 65 or 105.
posted by sour cream at 10:51 AM on May 29, 2007
My great-grandfather was an engineer and farmer in Southern Indiana. He was the fifth person in Indiana to have a Masters Degree, which he was awarded in 1905 from the University of Illinois. His masters thesis? Vedic Math's application in modern (1905) Western engineering.
He could do any math problem in his head faster than anybody with an adding machine or slide rule all from Vedic tricks.
posted by Pollomacho at 11:45 AM on May 29, 2007
He could do any math problem in his head faster than anybody with an adding machine or slide rule all from Vedic tricks.
posted by Pollomacho at 11:45 AM on May 29, 2007
I can’t remember where or how I learned this but I can do cube roots in my head that are derived from two digit numbers i.e. 185193 is 57. It is an easy math trick where the last digit of the cube of one digit numbers corresponds to the last digit in the problem and the first three digits are in the range of numbers not to exceed the next single digit cube. See easy. Here is a cheat sheet
2=8
3=27
4=64
5=125
6=216
7=343
8=512
9=729
Once you learn this it is easy; in our example the cubed number 185193 ends in 3 which corresponds to the last digit of the cube of 7 being 3; therefore the second digit is 7. The first three digits 185 are greater than the cube of 5 at 125 but less than the cube of 6 at 216 therefore the first digit is 5. By learning this simple table you can do cube roots of two digit numbers in your head. Other than mental masturbation and to confirm to your friends that you are an idiot savant, or as a chick repellant I am not sure what good it does.
What ever you do don't try this in a street fight. "Back off man I can do cube roots," unless you are wearing a bow tie, it scares the hell out of them.
posted by MapGuy at 7:43 PM on May 29, 2007
2=8
3=27
4=64
5=125
6=216
7=343
8=512
9=729
Once you learn this it is easy; in our example the cubed number 185193 ends in 3 which corresponds to the last digit of the cube of 7 being 3; therefore the second digit is 7. The first three digits 185 are greater than the cube of 5 at 125 but less than the cube of 6 at 216 therefore the first digit is 5. By learning this simple table you can do cube roots of two digit numbers in your head. Other than mental masturbation and to confirm to your friends that you are an idiot savant, or as a chick repellant I am not sure what good it does.
What ever you do don't try this in a street fight. "Back off man I can do cube roots," unless you are wearing a bow tie, it scares the hell out of them.
posted by MapGuy at 7:43 PM on May 29, 2007
Two significant digits is plenty. If you need more, then you probably have a pen handy.
85*85 => 80*90 = 7200.
posted by ryanrs at 2:38 AM on May 30, 2007
85*85 => 80*90 = 7200.
posted by ryanrs at 2:38 AM on May 30, 2007
Pollomacho wrote: He was the fifth person in Indiana to have a Masters Degree, which he was awarded in 1905 from the University of Illinois.
That seems odd. By 1905 Indiana had several well established universities (Notre Dame, Indiana University, Evansville, Purdue, etc).
posted by ryanrs at 3:30 AM on May 30, 2007
That seems odd. By 1905 Indiana had several well established universities (Notre Dame, Indiana University, Evansville, Purdue, etc).
posted by ryanrs at 3:30 AM on May 30, 2007
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posted by alexei at 12:21 AM on May 28, 2007