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Ishaan94
 3 years ago
Whom of you can explain it to me?
http://jeremykun.files.wordpress.com/2011/06/triangleproof.png
Ishaan94
 3 years ago
Whom of you can explain it to me? http://jeremykun.files.wordpress.com/2011/06/triangleproof.png

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Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0http://mathoverflow.net/questions/8846/proofswithoutwords/69756#69756

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0If it's fairly easy and you think I am not pushing myself please do tell me, instead of giving out the answer.

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3@Ishaan94  do you know how to get the sum of all the components in the last triangle?

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0Is it like this? (2n+1)+2(2n+1)+3(2n+1)+...+n(2n+1)

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3exactly  now factor out the (2n+1)

hosiduy
 3 years ago
Best ResponseYou've already chosen the best response.0i think like this way: i will assume that this is true until line n+1 (go downward from first line), i have: first line is true, 1+n+n = 2n + 1. so with line: n+1 we have: (n+1) + ... (n+1) at first triangle, at second triangle, we have: 1+ 2 + ... + n+ n+1, and at third: n+1 + n + ... + 1, sum last line, we still get: 2(n+1) + 1 + .... 2(n+1) + 1

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{n\left(n+1\right) \left(2n+1\right)}2\]What about the six?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3that is correct  now you have to subtract the sum of the previous 2 triangles from this

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3what you are trying to find is the sum of the numbers in the 1st triangle

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3that should have started with \(1^2\)

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3it is a visual proof of this sum

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3It's an interesting proof  I suggest you try and do it yourself  you'll have greater pleasure from that :)

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0thanks, i will try my best.

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3let me know if you require a clue.

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3when you do "see" how to do it  it is quite remarkable!

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3@Ishaan94  try turning your head as you view the triangles on the left...

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3this really is a "visual" solution  so don't think about any complex math here

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0OMG this is the best proof I have seen in my life so far

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3:) glad you "saw" it at last!

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.3it is a very pleasing proof

Ishaan94
 3 years ago
Best ResponseYou've already chosen the best response.0it is. and thanks a lot asnaseer. :)
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