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

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Ishaan94Best ResponseYou've already chosen the best response.0
http://mathoverflow.net/questions/8846/proofswithoutwords/69756#69756
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
If it's fairly easy and you think I am not pushing myself please do tell me, instead of giving out the answer.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Ishaan94  do you know how to get the sum of all the components in the last triangle?
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
Is it like this? (2n+1)+2(2n+1)+3(2n+1)+...+n(2n+1)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
exactly  now factor out the (2n+1)
 one year ago

hosiduyBest ResponseYou've already chosen the best response.0
i 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
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
\[\frac{n\left(n+1\right) \left(2n+1\right)}2\]What about the six?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
that is correct  now you have to subtract the sum of the previous 2 triangles from this
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
what you are trying to find is the sum of the numbers in the 1st triangle
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
that should have started with \(1^2\)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
it is a visual proof of this sum
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
It's an interesting proof  I suggest you try and do it yourself  you'll have greater pleasure from that :)
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
thanks, i will try my best.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
let me know if you require a clue.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
when you do "see" how to do it  it is quite remarkable!
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Ishaan94  try turning your head as you view the triangles on the left...
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
this really is a "visual" solution  so don't think about any complex math here
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
OMG this is the best proof I have seen in my life so far
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
:) glad you "saw" it at last!
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
it is a very pleasing proof
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.0
it is. and thanks a lot asnaseer. :)
 one year ago
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