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)
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......