Tuesday, May 29, 2012

Hardy–Ramanujan number

We all have read the story of Sir Srinivasa Ramanujan in our school time.
This is refreshing revision to it :

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was a renowned Indian Mathematician. Inspite of having no formal training in pure mathematics, Ramanujan made substantial contributions in the areas of mathematical analysis, number theory, infinite series and continued fractions. He independently compiled nearly 3500 results during his short life time.

1729 came to be known as Ramanujan number, after an interesting incident that took place between Ramanujan & his mentor, G. H. Hardy.

Hardy was paying a visit to Ramanujan, who was ill and undergoing treatment at Putney (London). Hardy mentioned to him that he rode a taxi cab, whose number was 1729. "...the number seemed to me rather a dull one", he added.
It is said about Ramanujan that the numbers 1 - 10000 were his "personal friends". He could effortlessly tell you their factors, divisors, how the number can be split & the each part of the number can be squared/cubed, etc. to produce interesting numbers, and much more.
Interestingly enough, Ramanujan replied to Hardy's comment, saying that 1729 is not a dull number at all. It is the smallest number that can be written as sum of 2 cubes, in 2 different ways.

This is what Ramanujan meant.
Ramanujan number 1729

After Hardy related this incident to his colleagues, this number became well known and was called as Ramanujan Number.
Later on, numbers having similar property were all called as Ramanujan Numbers & the problem of finding such numbers came to be known as TaxiCab(2) problem. That is, solution to TaxiCab(2) yielded numbers of the kind
a^3 + b^3 = c^3 + d^3

Here are a few numbers of this kind :
Ramanujan numbers

Numbers of the kind a^3 + b^3 = m^3 + n^3 = x^3 + y^3 are now known as Ramanujan Triples. The corresponding problem is known as TaxiCab(3).
Numbers of the kind a^3 + b^3 = c^3 + d^4 = w^3 + x^3 = y^3 + z^3 are known as Ramanujan Quadruples or corresponding problem is known as TaxiCab(4), and so on.

Moral of the story :
Infinite RESPECT is actually defined in the world !

Thursday, May 24, 2012


Three statisticians went hunting in the woods.

Before long, one of them pointed to a plump pigeon in a tree, and the three of them stopped and took aim.

The first fired, missing the bird by a couple of inches to the left. Immediately afterwards the second fired, but also missed, a couple of inches to the right.

The third put down his gun exclaiming, "Great shooting lads, on average I reckon we got it."

Moral : Don't work too much.You mind becomes mono-directional.Take breaks in life and enjoy it.


Coke and Pepsi

In the 1980’s the two big soft drink giants Coke and Pepsi were in business in USA. Both companies had good management.

Every meeting of the Pepsi and Coke teams in their conference hall used to be towards taking over the market share of each other. Very soon they realized that they were not making any headway in boosting their sales or profit.

But Coke team realised their mistake and changed their strategy. So Coke changed their agenda now to get their own sales and profit to increase by 0.1 % every month. In fact, their endeavor now was now to compete against their own capabilities.

The Coke company was initially succeeding in achieving their goal of 0.1 % increase in sales monthly. But after a few months the company found that even this small 0.1% increase in sales becoming difficult to cope with.

One day the CEO of Coke thought to change the strategy once again. He did a market survey to find out what is the total consumption of fluids of an average American.

The results were amazing. Each American drinks about 1.5 liters of fluids including water, tea, coffee, beer etc a day on an average and out that only 30 ml was soft drinks like Coke and Pepsi.

Now their conference was concentrating only on how to increase this 30 ml quota to at least 300 ml to start with. One of the executives suggested that they should make Coke available to the people when ever and where ever they felt thirsty or wanted to drink some thing.

To this end, Coke put up vending machines at every street corner. Coke sales were up more than ten times from then on and Pepsi has never quite caught up since.

Moral of the story : “Challenge and compete against your own capabilities, if you want to excel.” 

Wednesday, May 23, 2012

Balika vadhu and Soaps

This is a post to demonstrate 'LIVE' the effects of daily soaps like BALIKA VADHU.

After my office hours,i go for dinner at Dilipbhai's tiffin service(actually his home).He and his wife serves really good home-made food and that too at decent rate.

His house is a two storey building in which dilipbhai's parents stay on the first floor and dilipbhai himself stays on 2nd floor.

Sometimes i dine as early as 6.30pm but since people here are still orthodox,i have to dine on the first floor at dilipbhai's parentswala floor.

They daily follow a soap called BALIKA VADHU on COLORS Channel.
The word for that soap is BULLSHIT.

I have literally observed that dilipbhai's mother watches soap very intensely and she applies the reel situation in her own house on her daughter-in-law.

Both dilipbhai's parents have became sick as far as human nature is concerned and this is due to these bloody saas-bahu soaps.

If we apply simple calculations,that society contains such 50 homes and there are such 50 societies in satellite area(this is the minimum count).Suppose there are 10 such areas in ahmedabad then the total people involved in such atmosphere is 50*50*10 * 4(parents and son-wife) =1 lakh.

Even if literacy rate is 50%,then also 50,000 people get SICK due to these soaps.Mind well i am not considering the children here because ultimately they also get affected because their mother stays under depression due to such in-laws thinking.

Moral of the story : Please stop watching the daily soaps and make people stop watching it.Even a small change would change many lives :)


Wednesday, May 16, 2012

Decision Making

The story given here is quite interesting and really gives us an insight into decision making :

A group of children were playing near the railway tracks,one of them was active track while the other was disused.Only one child played on the disused track,rest on the operational track.

Suppose you are the driver of the train and you are just at the track interchange.
You could make the train change its course to the disused track and save most of the kids.

However,that would also mean that the lone child playing on the disused track would be sacrificed. Or would you rather let the train go its way ?

Think over this situation for 2 minutes(10 times the original action time).

Most of the people would divert the train to sacrifice only one child.To save most of the children at the expense of only one child was rational decision most people would make,morally and emotionally.

BUT,have you ever thought that the child choosing to play on the disused track had infact made the right decision to play at the safe place ?

Nevertheless,he had to be sacrificed because of his ignorant friends who chose to play where the danger was.

This kind of dilemma happens around us everyday.In the office,in community,in politics,and especially in the democratic society,the minority is often sacrificed for the majority no matter how foolish or ignorant the majority are,and how farsighted and knowledgeable the minority are.

The child who chose not to play with the rest,on the operational track was sidelined.And in the case he was sacrificed,no one would shed a tear.

To make the proper decision is not try to change the course of the train because the kids playing on operational track should have known very well that the track was still in use,and that they should have run away if they heard the train's sirens.

If the train was diverted to the disused track,we could put the life of all the on board passengers at stake.And in your attempt to save a few kids by sacrificing one child,you might end up sacrificing hundreds of people to save these few kids.

Moral of the Story : What's right isn't always popular and what's popular isn't always right !