Monday, September 15, 2008
Yep, that’s right too!! It’s a 150 year old problem. For 150 years the best minds of the world tried to solve this problem and came up short. The great minds were convinced that a solution to this problem exists but were unable to find it. Even taking the aid of high performance computers couldn’t help the matter. Now, you must be thinking-“what the big deal about a damn puzzle!!”. Well, to answer that you have to understand the puzzle.
Let get introduced to the hardest unsolved problem in mathematics since 1859---“REIMANN HYPOTHESIS”.
And yes, I didn’t forget about the $1 million. Boston Clay Mathematics Institute declared in 2000 a list of 7 unsolved problem of mathematics. For each problem $1 million was announced as prize money. Since then 6 problems have been solved and the 7th and the most important one is still waiting.
In 1859, Bernard Reimann published his eight page article where he discussed this idea. It’s about prime numbers. So, let’s dig into the problem.
Prime numbers are type of numbers which can be divided only by 1 and itself. The series of prime numbers look like this.
1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73…and so on.
You can clearly see it. It is NOT a series. There is no sequence in the numbers. We can’t say what will be the number next to 59 without calculating individually each number. To make my point clear consider the following series, which is actually a series.
We can see the sequence and we can also deduce the last number, it is 196. For the mathematically challenged people the series is simply the square values of natural numbers i.e. 1, 2, 3, 4, 5…and so on. We can even say what will the 500th number of the series without checking the in between numbers. By this definition the prime numbers do not constitute a series. It’s too haphazard.
But it is also mathematics. Mathematics can’t be haphazard. There must be a method in madness. People (not normal people, mathematicians I mean) tried and failed to find a formula of prime numbers. In a desperate attempt to find any resemblance of order they tried to find the occurrences of prime numbers. See for yourself.
In 1 to 10 there are 4 prime numbers, which means 40%, so there should be 40 prime numbers in between 1 to 100, but there are 25 actually i.e. 25%. In case of less than 1000 it is 168 or 16.8%.
And between 9999901 to 10000000 it is just 9. The next 100 contains just 2. This was a total chaos.
But, there are some who do not conform to the norms. They think in their own way using their own logic. We call them genius.
One such genius was Leonardo Eular. This guy found an order where seemingly everyone had failed. What he showed was not only remarkable was incredibly easy too.
1+ 1/2^2 +1/3^2 +1/4^2 +1/5^2 +⋯=2^2/(2^2-1)*3^2/(3^2-1)*5^2/(5^2-1)*7^2/(7^2-1)*…
It was really wonderful. On the left hand side was natural numbers like 1, 2, 3, 4…..and on the right side was the prime numbers 2, 3, 5, 7…..
There was an order here. It was a start, but wasn’t an end. This equation was developed further and it was proved that the power of the numbers is not only limited to 2. It can be raised further i.e. the following equation will also hold true
1+ 1/2^3 +1/3^3 +1/4^3 +1/5^3 +⋯=2^3/(2^3-1)*3^3/(3^3-1)*5^3/(5^3-1)*7^3/(7^3-1)*…
and also if the power is 4, 5, 6 anything.
Now, the stage was set for Mr. Reimann to appear and did so in style. He developed the equation one more step and proved that the power of the numbers is not only limited to natural numbers, it can be complex numbers too i.e. the equation will hold true even if the power is a complex number.
Complex numbers are numbers which are created using rational and √-1. √-1 is square root of -1 which is an imaginary number.
Now, the question that naturally arises is that WHY THE HELL DID HE USED COMPLEX NUMBER????
Well, the answer to this question is the topic we started on. Reimann kept on developing the equation and discovered this
1+ 1/2^(0.5+7√-1) +1/3^(0.5+7√-1) +1/4^(0.5+7√-1) +1/5^(0.5+7√-1) +⋯=0
The most important aspect of this equation is that the co-efficient of √-1, which is 7 here, is of NO IMPORTANCE.
Yes, you read it right. It is of no importance as long as the first rational part is 0.5. You can change the co-efficient to anything you like, positive, negative, fraction, real anything, it doesn’t matter.
So, this is also same as the above.
1+ 1/2^(0.5+3√-1) +1/3^(0.5+3√-1) +1/4^(0.5+3√-1) +1/5^(0.5+3√-1) +⋯=0
This is Reimann Hypothesis. But it is never going to be possible to physically check every number imaginable to see if the equation works. Reimann said that the equation will be equal to zero if the rational part of the power is 0.5 and the co-efficient of the irrational part is any number. That was 1859.
150 years passed. So many other problems were solved using Reimann Hypothesis. They are proved as “if Reimann Hypothesis is true, then……”. So, if those answers are right then Reimann Hypothesis must also be true. But that doesn’t solve the problem. It has to be proved using mathematical logic and the quest still eludes the man. Solve it and the glory is yours. 1 Million dollars doesn’t hurt either!!
Thursday, September 11, 2008
The tall guy was sitting under a tree in a park; sipping tea and thinking about the inflation and the grocery bill. Suddenly something dropped on his head.
He looked upwards and discovered an apple tree and looked downwards and discovered gravity (figuratively speaking of course!).He published his findings in “Philosophiae Naturalis Principia Mathematica”
I was sitting in my friend’s house, sipping tea and talking about joining date of TCS and music of “Rock On!!” and listing to Debankar’s guiter .Suddenly something dropped on my head. I looked up and discovered a disk of “Munnabhai MBBS ”. I looked down on the disk and discovered copyright.
Actually I didn’t discovered copyright; I discovered the disk was original. Now that’s a bit complicated, what the hell original disk means? Most of us go through life without seeing a single original disk of anything i.e. movie, software etc. And here in my hand was an original piece, written behind “buy original CD or DVD, kill piracy”.
I heard so many times on TV, radio that musicians are requesting people to buy music and save their livelihood. I also saw people saying copyright means my right to copy. I looked at my computer, it was starting up. The OS was pirated Windows XP. The anti-virus was pirated; most of the softwares I use are pirated. Almost all the songs that sit on my machines are copyrighted and haven’t paid anything for them. The movies I have watched till now were all pirated. Where that does leaves me? In fact everywhere I look I see rampant copyright violation. I tried to calculate the damage done to entertainment industry by me. It came to around 500 movies and so around 20000 bucks. I alone cost that much!!! That too without considering the songs or eBooks collections that I pride myself. I didn’t dare to calculate further.
Then something struck me. I never heard any musician or author (of course of modern times) dying of starvation. That obviously doesn’t mean anything. I decided to probe further. An audio CD costs around Rs.100. Which is not very cheap considering it contains around 8-10 songs all of which are not good, whereas one can download it for free. And there is not much difference between qualities. So the choice is between high priced over hyped products and free illegal materials. No prize for guessing the winner.
I remember about a particular incident. It was 19th July 2007, Harry Potter and deathly hallows was to come out 2 days later and I was already reading it in eBook format. When it finally came out I have finished it by then. Now, if I was author it would be terribly distressing to know that my creation wasn’t fetching me anything or will it be? It would also probably mean that people like my writing so much that they are willing to suffer damage to eyesight by staring to computer monitor to read a book!!!
Actually it is very difficult to find a solution. One possible solution could be to lower the prices of original pieces or maybe to make the quality of original pieces better so that copying them damages their quality.
Its no point crying over piracy, otherwise it wasn’t possible to listening songs or watching movie so much. So, keep on doing whatever you do, just be careful to avoid using traceable downloads. CHEERS!!!
Wednesday, September 3, 2008
The times couldn't have been more exciting for net-addicted people like me;two new browsers are soon going to be launched and their beta versions are already available.
First,the old and much abused Internet Explorer is coming out with IE8.Its simply amazing to think how a once great corporation can come out with a worse version and declare it a new version.This happened with IE7;it was worse than IE6.Maybe it was more secure or things like that but its speed was awful.Hope that IE8 fares better.
Second and most important is Google Chrome.The product from the stable of the undisputed rulers of web world.I tried its beta version and its excellent.Its lightweight(takes very little resource) and slick.The only problem I can see is the customization options are very limited.Maybe it will be taken care of in the stable version.
Anyway thst was just to keep this blog alive.When the two browsers come out with their stable version I will write about them.
Friday, July 4, 2008
When I first started writing this blog,I thought I would steer clear of any political topics. But living in modern
CPI(M) is Indian's one of the few national parties. The following points are some questions raised from time to time against them.
The communists were opposing the British rule with the rest of the country. Then
2.1962 India-China war
This was probably the best example of Indian communist's mentality.
3.1998 Pokhran Nuclear experiment
As usual CPI (M) opposed
Not only these, every time the communists oppose something they give same reasons as the Chinese do.
In such circumstances it will be better if the Communist Party of India changes its name to Communist Party of China based in
I am waiting for your comments.
Tuesday, April 8, 2008
First I must give the specifications of my machine.
Its a 6 year old P4,192MB RAM,40 GB HDD computer running Windows Xp SP2.And being true to a guy mentality I am going to compare them with girls.
Lets start with the default browser.
Internet Explorer 6
Its the default browser of Windows.Much abused and the last fall back.Its like house maid.They are inefficient,security threat,lazy,a burden but very strong.Any user knows IE6 can and will probably break down at every inopportune moment,but they are indispensable.Not much to write about it.77% of user use it.Its steadily declining though,from 95% in 2002.Still its the primary browser.Probably because most people donot bother to install another browser.They use what they get.So,be assured IE6 is not going to die soon.
Internet Explorer 7
I don't know what possessed Microsoft to make this Dinosaur.Its like a good looking and lazier maid.Thats all.Its security is better(they claim,you won't understand it).Speed is slow definitely,despite whatever they say.In short.it is worse than IE6.
One of my best friends put it best.Safari is like a good looking girl on your way who deserves a second look.Nothing more.Its fabulously good looking.Pretty fast,efficient.The new version is stable and most importantly it comes from stable of Apple.So,service is going to be excellent.Still it doesn't score much with me.Why?Simply because it is not much customizable.Just some limited options.You can't bend it to your will.After all,every beautiful woman can't be a good partner.
This one is the most beautiful,gorgeous,stylish and efficient.In other words.....perfect.Its has innumerable features,faster than most,excellent service,breathtakingly beautiful.It has inbuilt torrent tracker,downloader,voice identifying property,256 bit encryption for security and what not.No other browser has so much features and so much efficient.It only has one small problem,Orkut doesn't load very fast.And most of the sites cant keep up with its security features.So,you have to keep them disable mostly.Debankar,the great computer-wizard,put it best(again,as usual) its only good for some extra marital(surfing) affairs.But if you can keep up with it,go ahead.Its the best.
This thing scores where Opera can't.Its a social networking web-browser(never heard about them,may be they will come up with a youtube viewing web browser next).Its pretty useless.Yes,thats right.Its useless,unless you happen to be that type of person who have 300 friends on on net and remains 10 hours online a day.It uploads pictures fast and some necessary accessories for social networking sites.My advice:you can definitely try it.you have nothing to lose.Oh,I forgot.Its basically a modified Firefox.
Its the best if you are ready to change.Biggest competitor of IE.Its interface is easy.totally flexible.Its freeware,so you can develop new add-ons for it.Its fast,efficient,flexible,doesn't grumble much.With add-ons it can be made to look beautiful.Moreover its quite homely.Everything a wife should be.Its got 17% users using it and its growing.The biggest strength lies it in flexibility.You can do whatever you want to do with it.The only problem is that it takes ages to start and sometimes it just crashes.Otherwise an excellent choice.My personal favorite.
Thursday, April 3, 2008
I was thinking about writing about this for a long time. It is about those friends who are girl but not girlfriends. I have been blessed enough to have such terrific friends that it would be gross injustice to not to write about them.
The first thing that sprang to mind is “impossible”. Yes, they are indeed so. Impossible and unreasonable. And nice enough to make you bend to their weird wills and impossible demands.
But, well, world would not have been same without these impossible and unreasonable women. Life not only would have been dull but difficult too. Just imagine a day with no one to irritate or no one to chew brains and most importantly, no one to pour your heart out.
Yes, these are the friends who will be the first to find your fault and the last to criticize you. They will get irritated by your skirt-chasing and then will point out the better ones. First to console in your grief and first to rejoice your happiness. Encouraging you to go on despite failure and always keeping faith on you even when you yourself do not. Most importantly, they will make you realize that you don’t need to be perfect.
On the other hand you will have to face their sudden mood-swings, very weird sense of humor (the most inappropriate things seems funny to them). At times, they can be more difficult than babies, refusing to heed anything.
But still, they are those great friends whom you can trust with your life and come out alive too, a great blessing in the competition-centric world of today. If you don’t have such a girl friend you will probably never understand what I mean. And if you have one……………………..well…………..I don’t need to explain anything then.
Waiting for your responses to this topic. I really want to know what you think about it and especially girls view-point.
Wednesday, April 2, 2008
The man turned around and looked at the frog.He couldn't believe his eyes.The frog again said "Please kiss me and make me a beautiful princess".
The man came forward and took the frog in his hand.then he stuffed it in his pocket and started walking.The frog cried out from his pocket"aren't you going to kiss me?"
The man replied
"I am an engineer.I don't have time for a girlfriend,but a talking frog is cool".
Engineers are like this.So, girls please beware of them.In any case he can easily leave you for a Intel Quad-core Macbook pro.You can never hope to match its performance.
Monday, March 17, 2008
Now, to get any type of transport to go anywhere, I must reach Ruby. That was 20 minutes walking and no transport was visible. I blinked at the dazzling sunlight and tried to think a solution. Unable to find one I recounted that famous line
“A journey of thousand miles begins with a single step”
and took the first step. It landed on a broken brick. After cursing that unfortunate brick (it was smashed under my weight) and its maker I started trudging.
After 10 minutes I barely covered 100 meters and was panting like dog. The sun was very benevolent, and finding shadows was harder than finding
After 20 minutes, I covered half the distance and decided that I should take rest if managed to find a shadow. I soon found one under a tree and rushed there. Rushing was not necessary as no one was in sight and the tree was not in any risk of being chopped down before I reach there.
While I should there, I managed to attract the attention of a female. She was looking at me with her bright green-blue eyes.[I know girls die for me and you don’t need to smirk; I appreciate complements].After contemplating for a few moments she decided to come nearer. I stroked her back and she meowed back.
[Now, don’t take it otherwise, but I love cats]
Soon, lorry was passing by. Seeing that and probably sensing that I have nothing to interest her gastronomically (ungrateful females!!!) she jumped on a fence and went away.
I started trudging again. A rickety dog started following me. I suspected that it was a member of anti-Cat Action Team (aCAT) and has probably labeled me as a cat-lover therefore a dog hater.
I discovered a biscuit in my bag from someone’s
Sunday, March 16, 2008
It was a hot day. I was sitting in the college, idly as usual, when “THE” idea struck me. As the creative person I am, the idea still seemed like a 440 volt one.
I am going to bunk college.
Now, even the historically challenged readers can also point it out that colleges are being bunked right through its conception. So, what is so special about the idea?
Well, I can just say that I decided to bunk, now I have to find the reasons too. Life is not at all easy!!!
I tried to think some and these jewels came out!!
- I have not done anything useful in the first few classes and probably will not do anything useful again in the next classes also.
- There was not any practical class. Now, practical classes are useful for the purpose for chatting while playing the mindless game of PINBALL. It was our equivalent of coffee house (sans coffee, of course) where one can indulge in a vigorous session of adda.
[Though to be truthful, the labs are not for adda only. Some humorless, unsympathetic and curtsy less teachers think otherwise and makes it such a place where one cannot play PINBALL]
- There were only 17 students present. If I leave, I may influence some others to leave also. That will decrease the population (of class, not
) and may encourage the college to suspend classes. India
In fact, this last reason seemed brilliant to me. I congratulated myself for my logical and most brilliant thinking. I was tempted to point these out to anyone who was even remotely interested (there was none) but spied the teacher coming towards our class. So, I had to stop patting my own back and grabbed my bag, got out of the class back door, through the back corridor, by the back staircase and then the back door of the building and finally through the back gate of campus, I emerged on the road. My journey has started.
Tuesday, March 4, 2008
The life in camps in more than a life,its actually a culture,so many type of people living at the same place with distinct identites.It makes a melting pot, it's a culture with its own norms and values.
The biggest thing overall the commonalities of their rearing are so powerful ... It's an identity that supersedes almost all others. It cuts across lines of gender, race and class. It shapes us our entire lives through.
These people are shaped by their upbringing. There are numerous commonalities (both positive and negative) that impact them. Because of these factors, they often feel like "outsiders."They often feel like they have no home and never truly fit in with civilians.To put in a nutshell they dont have a sense of belonging to anywhere...atleast for me it is so.
So,its gets kind of difficult to settle in a life anywhere when you dont have that sense of belonging.You always try to find that place ...your place.....and never seem to find it....People never seem to understand you,and unintentionally keep hurting you.
When I was growing up,my life got shaped by uncertainity.There was uncertainity about father's job too.He never knew when he have to go or when he will be at home.In fact it was a favorite game of me and my mother:when father is going to return;nd most of the time he didnt return as predicted!!!!
Changing home so many times,changing schools again and again that many means i never had any steady set of friendz,every time we shifted i had to start from scratch;making frndz agian,moulding myself like them.....assuming a new identity.
So many things happened at short notices,I changed my school and actually completed the later part of the year in another school!!
Too many thaings happened during this time which changed me.
But one thing for certain.....
So,I am writing this blog ...not somewhere smoking grass or doing something like that.
P.S. I decided that I am not going to write everything about me;afterall somethings are too personal.The memories which cant be shared,the anecdoted which cant be recounted............so many things....
It makes me wonder......so many days passed...so much happened....
So,I am just going to review some things and discuss about some other things.Hopefully you will keep faith!!!!
Good bye for now....
Saturday, March 1, 2008
“Why are you wasting time on me!! Tomorrow there will be better friends than me, better appreciator of your beauty and your virtues. Why the world should waste time on me!”-Anonymous
[This is MY story. So abandon hope all who reads this]
(What you read on the following pages is true to my personal knowledge, but I can furnish no proof for most of them. So it is advisable to either take everything at face value or consider it as chin-wagging of a crazy person and give no more importance than that)
My father was a pharmacist of BSF. He got a govt. job in
On the other hand, my mother’s family was 47’s refugees. They were from
So, I am a son of an immigrant and refugee family. These families have something very common between them; they all know they have neither the financial capability nor the social status to help their wards to establish. So they lay great emphasis on education. Normally these people are very gentle & law-abiding, perhaps not to outrage the country which helped them.
These people, who are called “Bangal”, have a tremendous competition with “Ghati”, who are the original residents of
Sorry for the long absence,actually i was searching for answers...questions were a so much ,answers none.So,I just took a break and tried to find my inner demons.Things of which I was frightened ,things I couldn't face,things I....well.....probably you all know the feelings .
So I decided to review my whole life..the result is an autobiography.
Now ,as in all autobiography...I wont be telling all the truths.....but most will be written from heart
You have to take them at face value.......with tongue firmly in cheek....
So,lets get started......
As the announcer announces........
HERE COMES THE MOST AMAZING THING EVER THAT WALKED ON TWO LEGS---------ATANU ROY!!!!!
Monday, February 25, 2008
So,we saw that 11 and 9 have a common property in division,so have 16 and 6.Did you notice a thing?When multiplied they come to near 100.Right!!!
Nearer 100 ,more accurate the result is.So
for 100 we get pairs as 20&5;25&4;50&2;You can see any number divided by a number will result in the multiplication by the other number of the pair.For 100 we get the perfect result.
For 99 we get 11&9........we already saw,they give fairly accurate answer.
For 98 we get 14&7;49&2...we checked by 14 and 2 earlier...its quite accurate.So is 49 &2
For 97....ummm.........unfortunately ..its a prime number...
For 96 we get 16&6;48&2;24&4;12&8;...we checked by 16&6....the error gets quite hight;its only correct to a single decimal place.So,the error starts to get picked up.
If you go on further the error will be picking up so the result will be not so accurate,but it will be still workable....
So,keep this small thing in mind and sail through the calculations.
"Nearer the 100;more accurate" and "division by one number results in multiplication by the other number of the pair"
Tuesday, January 15, 2008
When many people say how many of Sachin's hundreds have come for a winning cause,Here is analysis of each of those centuries he scored when INDIA lost and reason why it went in vain.
Out of the 41 hundreds, 11 hundreds have gone in vain.
1. 137 off 137 (Strike rate 100) balls Vs SriLanka at Delhi in 1996 World Cup.
India scored 271/3 in 50 overs. The only other 50 score was from Azhar. SL made 272 in 48.4 overs. Manoj Prabhakar had 4-0-47-0. He also opened in the innings and scored 7 of 36 balls.
2. 100 of 111 Balls Vs Pak in Singapore- Apr 96.
India 226 all out in 47.1 overs, When Sachin was out score was 186/4 (We cant blame because next 3 are match fixtures) . Pak had a reduced target of 187 from 33 overs.
3. 110 of 138 Balls (Slower but...) vs Sri Lanka In Colombo - Aug 96.
Again India 226 for 5 in 50 overs, Only other 50 score from Azhar (58 of 99 balls !!!) .Sachin has also bowled 6-0-29-1 , the second most economical bowler and the only wicket taker (SL were 230/1 in 44.2 ) of the match next to Srinath. 7 bowlers were used by Azhar.
4. 143 of 131 Balls (!!!) Vs Aus at Sharjah, Apr 1998.
This was chasing under lights. The qualifying match before the final. The whole world knows about this match. Still one interesting point, when Sachin was out India were 242 at 5 at 43 overs. Target was 276 in 46. Still India finished at 250/5 scoring just 8 of the next 3 overs. Great performance by Laxman and Kanithkar indeed.
5. 101 of 140 Balls against SL at Sharjah in Oct 2000.
Indian score was 224/8 in 50 overs. (No other 50 score). SL got 225/5 in 43.5; Sachin also bowled 5-0-22-0, better economy rate than everyone except Srinath.
6. 146 of 153 Balls against Zimbabwe at Jodhpur - December 2000 (Game of Dougla Mariliar) India made 283 / 8 in 50 overs. Sachin was the last man to be dismissed, score was 235/8 at 46.3 overs when he was out. Agarkar and Zaheer Khan propelled India to 283 in the last 3.3 overs. When Sachin has scored 146 of 235 in 46.3 overs, you can guess what the other 8 great batsmen were doing against the World class Zimbabwe attack. Second Highest scorer was Zaheer Khan with 32.
Zim got 284/9 in 49.5 overs. Kumble bowled the last over. Sachin also got 6-0-35-1
7. 101 of 129 Balls Vs SA at Johannesburg - Oct 2001
India got 279/5 in 50, Ganguly made 127 of 126 balls. When Ganguly got out, the score was 193-1 in 35.2 overs. Sachin was the last man to get out at 263. SA got 280 in 48.4 overs. Sachin bowled 9-0-51-0, second best in economy rate next only to Agarkar (10-0-45-1)
8. 141 of 135 balls Vs Pak at Rawalpindi, March 2004
India was chasing 329 and was 317 all out in 48.4 overs, 8 balls to spare. No other batsman made even a 50 (when chasing 300 ) and when Sachin was out, India were 245-4 in 38.4 overs. They needed 85 from 68 balls with 6 wickets in hand.
9. 123 of 130 Balls vs Pak at Ahmedabad, April 2005.
India made 315/6 in 48 overs (48 over match), again no other 50 score. Second highest was Dhoni 47 of 64 balls, (third highest was extras - 39). Pak made 319 in 48 overs. The three quicks (Balaji, Nehra and Khan went for 188 runs from 26 overs between them taking only 2 wickets). Sachin bowled 6-0-36-1. No Harbhajan and no Kumble.
10. 100 of 113 Balls Vs Pak at Peshawar, Feb-2006.
India were 328 all out in 49.4 overs. Pathan and Dhoni got 60 each. When Sachin was out when India were 305-5 in 45 overs. Managed only 23 in the last 5 overs.Pak scored 311/7 in 47 overs and won by D/L method. Could have been anybody's game. Sachin did not bowl.
11. 141* of 148 balls vs WI at Malaysia.
India made 309 /5 in 50 overs. Sachin was not out. Pathan was the only other 50 scorer. WI made 141/2 in 20 overs and won by D/L method. Again could have been anybody's game.
In the other 31 instances India has won 30 times and once there was no result.
Now for those people who say Sachin can't win matches.The truth is that India played a long time with 1 PLAYER and 10 JOKERS.
Tuesday, January 8, 2008
Division by numbers 1,2,3,4,5,6 are very easy and I wont take much time for it.
Division by 1:same answer
Division by 2:do it dumbo!!Its very easy....
so and so till 5
Division by 6:
Just see this
2/6=0.333 [ 16*2=32]
So,you can see its nearly the table of 16 on the decimal side,but the margin of error is quite high...
Division by 7:
Here it is table of 14
Here the margin of error is quite small and its quite easy to remember
Division by 11:
Here it is table of 9
This method can be applied to other numbers also..
Now come the fun part....
For the every number we get another number's table.If that number is used for the division then we will get the first number's table.Lets clear it with an example:
For division by 11 we use 9's table;Similarly for division by 9 we can use the 11's table!!!!
Now for quick reference the pairs are given,one can be used for the division by the other.
4 - 25
2 - 5
6 - 16
7 - 14
8 - 12
9 - 11
Now,have fun.......calculation is basically very easy,you just have to know what to apply and where.
Saturday, January 5, 2008
The return of Vedic maths is evident but there is this question of where exactly it returned from. Though the computational system is widely believed or perceived to be from ancient Vedic scriptures, there is no visible evidence to support that claim.
In the 1960s, Tirthaji Maharaj, who was the Shankaracharya of Puri at that time, said that he had found some verses in the Atharvaveda that led to astonishing methods of calculations.
It was he who wrote the first compilation that came to be called Vedic mathematics. Not everybody believes that the seer, who himself had a strong background in maths, had indeed found an old treasure. The material that the holy man claimed was part of the Vedas was a set of 16 cryptic Sanskrit verses that could mean anything.
For example, one of the "formulae" is Ekadhikena Purvena. When translated, it simply means, "By one more than the previous one".
But Tirtha Maharaj interpreted it in various ways and formed entertaining methods of easy multiplication. The entire Sanskrit text of what is called Vedic maths is not more than fifty words.
"It is a mystery how people do not notice such simple things," says SG Dani, a professor at the Tata Institute of Fundamental Research who believes that the whole saleable system of Vedic Maths is in reality just a set of interpretations of one man.
Dani once said in a public letter signed by several noted academics, that Vedic Maths is, "neither Vedic nor maths".
But whatever be its origins, nobody denies that the Shankaracharya is saving boys and girls a lot of time in their CAT practice tests. They may not escape the endless cycle of rebirths but may escape the cycle of retests.
3852 x 7 = 26964
Starting at the right (2), we double the first number (it has no neighbor) and write down the right-most digit of that (4) and we have no carry. Then we double the next number (2x5=10), add five (+5=15), and add half the neighbor (+1=16), and write down the right digit (6) of that and carry the 1. Then we double the next number (2x8=16), and add half the neighbor (+2=1, and add the carry (+1=19). Then we double the next number (2x3=6), add five (+5=11), add half the neighbor (+4=15), and add the carry (+1=16). Now we double a zero off to the left of our 3852 (theoretically the zero should be out there: 03852) and addhalf the neighbor (0+1=1), and add the carry (+1=2).And we have our answer.
Notice that the carries are smaller than they were innormal multiplication by 7. The above rule is not simple, but once mastered, it is easy to use. It should be about as fast as multiplying normally (which requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12) uses similar rules.
3852 x 7 = 26964
Starting at the right (2), we double the first number (it has no neighbor) and write down the right-most digit of that (4) and we have no carry. Then we double the next number (2x5=10), add five (+5=15), and add half the neighbor (+1=16), and write down the right digit (6) of that and carry the 1. Then we double the next number (2x8=16), and add half the neighbor (+2=1, and add the carry (+1=19). Then we double the next number (2x3=6), add five (+5=11), add half the neighbor (+4=15), and add the carry (+1=16). Now we double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.