Easiest proof to the 'Pythagoras Theorem...'.

I would begin this post with an apology...an apology to myself ,for not being regular coz it has been 10 days since my last post.But i will try to be to be regular henceforth.So what the hell kept me so busy that I could not find time to write a post?Actually,I had been to my workplace for some work and just returned yesterday.

Having worked with a genius , I can say that the past few days have been really beneficial for me.De facto,I can say that I got enlightened.And that is to be held responsible for it is the same genius.The genius I am talking about is Patrick(real name-Pratik ,a friend of mine).I regret not being in touch with him earlier...Nways its better late than never.

We discussed a lot of things(physics,theorems,algorithms,mathematics) while working,things which I never knew and would have never known had I not met him.Amongst those things ,I would like to share one.Its about the Pythagoras theorem.When was the last time you wrote a proof for the Pythagoras theorem?It must be a long time,probably u must have done that in 8th or 9th grade.Do you remember the proof?I bet only a few of you can.Here is one proof that you gonna remember for the rest of your life. Here is how it goes...

The Pythagoras theorem is ::
In a right angled triangle
( Hypotenuse)^2=(base)^2 +(height)^2
For any of the triangles shown in fig..

A^2 + B^2 = C^2

Consider two squares as shown in the figure aside

Area of the outer square=(A+B)^2
=A^2 +B^2 + 2AB ------>(1)

Area of the 4 triangles=4*(1/2 )*(A*B)
=2AB ------>(2)

Area of inner square=C^2 --------->(3)

Its a cliche from the figure....
(Area of outer square) -(Area of 4 triangles)=Area of inner square
Replace with (1),(2),(3)
A^2 +B^2 + 2AB - 2AB = C^2

which gives us
A^2 + B^2 = C^2

Now wasnt that as simple as 1,2,3...?I 'm not sure who gave this proof ,Pythagoras himself,Bhaskaracharya or Aryabhatta .It was Patrick who told me about it and I am grateful...
Thanks a lot...Bbye and God bless......


Anuprit said...

Nice 1! And yes, you will keep learning such things when you work with Patrik!

prashant said...

That's a proof not to be remembered.

ashwin said...

this patric is our once na???

akshaydeshmukh said...

@ashwin,yes he is our patrick...aur kaun ho sakta hai yaar...???

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