## The Funny Side of Mathematics

During my interview for IIM Indore, which coincidentally was my first experience of an “IIM Interview”, I yelled a few times that I am good at mathematics and I should be asked questions on that. I also mentioned I would like to teach mathematics etc etc, lets leave the details.

The learned professor, who was supposed to ask the tech( acads maths etc) questions suddenly asked, **” Can you prove 1=2?”.**

For a moment, I was like what? Then I told him that it is wrong thing, and all the proofs that you get in forwarded emails and fun sites are wrong and flawed.

He said, yes it is flawed, can you tell me the flaw?

I somehow ws not able to recollect this simple thing there, but I did it as soon as I was outside the room, interview blues I guess.

So the readers of this blog do not have such a problem, let me explain some ways to prove 1=2.

**Method 1**

x^2= x+x+x+x+x… ( x times)

differentiate both sides wrt x

then we get

2x=1+1+1+1+.. (x times)

2x=x

=>1=2

everything looks good, isn’t it ? But it is flawed. I leave it to the reader to figure out the flaw? if not, I will explain the flaw in one of teh comments. Kindly bear with me !

**Method 2**

1/4=1/4

(1/2)^2=(-1/2)^2

taking square root both sides

1/2=-1/2

add 3/2 both sides

2=1

This is much simpler and the flaw is also visible, i.e square roots are always positive .

**Found it funny? Not yet?**

One of my other friends was asked to tell **when is pie day celebrated?**

Innocent though he was, did not take a guess. You can always hazard a guess pie =3.14 so it has to be 14 march ( American calendar)

There is also a pie approximation day and yes you guessed it right, it is 22/7 that is 22 july ( english calendar).

**Ramanujam’s Number**

A friend of mine, who as well proclaimed himself as math wiz in one of the IIM Interviews, was asked tell me about 1729?

And he was a wiz? Yes you guessed it right. He answered it well. 1729=10^3+9^3=1^3+12^3

It is the smallest number which can be written as the sum of two cubes in two different ways. It is a very famous number, so if you dare to proclaim maths as your hobby, you must know it.

Want to more? wikipedia, my friend! ( Indians must know about Ramanujam)

Thats all!

Cheers1

Kindly tell me the flow in the differentiation method. I couldn’t think of 1.

VipulApril 7, 2009 at 7:11 pm

1=2 phew!!

x=2x

It means x=0

But x!=0 as 0/0 is undefined

ProblemSmokerApril 11, 2009 at 9:27 pm

Hi there,

I have started preparing for CAt 09. I came across your blog and i tht i’d get some tips from you. I am finding it diffcult to und the concepts of “Numbers”. Could you pls tell me which books to refer?

Thank

Sasti Kumar S.V.

Sasti kumar S.V.April 24, 2009 at 7:59 pm

I simply loved your blog.i was always prejudiced to maths. i am surprised that i could understand every bit of what you wrote. Thanku so very much.

sharonAugust 2, 2009 at 9:33 am

Hey Sharon!

Thanks for your comments!

I am happy that I may have helped you to forego some of your prejudices about Maths!

Rahul

RahulAugust 2, 2009 at 12:23 pm

hi Rahul.thanku for ur reply.

sharonAugust 3, 2009 at 1:33 pm

I desperately need someone to help me overcome my fear for the subject. I wish u could help me.I am

planning to take CAT .pls write more interesting stuff on ur blog[ur kind of stuff,not the cliche …..].good day,rahul.

sharonAugust 3, 2009 at 1:44 pm

yeah Sure!

I will try to put as many as possible!

RahulAugust 3, 2009 at 10:45 pm

hey.. can u pls xplain da flaw in dat differentiation method of proving 1=2..

deepak sharmaSeptember 25, 2009 at 12:06 pm

x^2=x+x+x+x+x+x+……..(x times)[This statement is wrong for all x<0 and for all non integral x]

it has to be x^2=x*x

Differentiating:

2x=x.1+1.x

2x=2x

harsh bansalFebruary 20, 2015 at 10:58 am